Information on Result #3178506
Digital (29, 32, large)-net over F128, using 4 times m-reduction based on digital (29, 36, large)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (26, 33, 8388602)-net over F128, using
- net defined by OOA [i] based on linear OOA(12833, 8388602, F128, 9, 7) (dual of [(8388602, 9), 75497385, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(12833, large, F128, 3, 7), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1280, s, F128, 3, 0) for arbitrarily large s, using
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
- linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1281, s, F128, 3, 1) for arbitrarily large s, using
- appending 2 arbitrary columns [i] based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(1281, s, F128, 3, 1) for arbitrarily large s, using
- linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code) (see above)
- linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code) (see above)
- linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code) (see above)
- linear OOA(1284, 699051, F128, 3, 2) (dual of [(699051, 3), 2097149, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1284, 2113665, F128, 3, 2) (dual of [(2113665, 3), 6340991, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(1284, 2113665, F128, 2, 2) (dual of [(2113665, 2), 4227326, 3]-NRT-code), using
- appending kth column [i] based on linear OA(1284, 2113665, F128, 2) (dual of [2113665, 2113661, 3]-code), using
- Hamming code H(4,128) [i]
- appending kth column [i] based on linear OA(1284, 2113665, F128, 2) (dual of [2113665, 2113661, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(1284, 2113665, F128, 2, 2) (dual of [(2113665, 2), 4227326, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1284, 2113665, F128, 3, 2) (dual of [(2113665, 3), 6340991, 3]-NRT-code), using
- linear OOA(1286, 699051, F128, 3, 3) (dual of [(699051, 3), 2097147, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1286, 2130049, F128, 3, 3) (dual of [(2130049, 3), 6390141, 4]-NRT-code), using
- linear OOA(12819, 699051, F128, 3, 7) (dual of [(699051, 3), 2097134, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12819, 2097153, F128, 7) (dual of [2097153, 2097134, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(12819, 2097153, F128, 7) (dual of [2097153, 2097134, 8]-code), using
- linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(12833, large, F128, 3, 7), using
- net defined by OOA [i] based on linear OOA(12833, 8388602, F128, 9, 7) (dual of [(8388602, 9), 75497385, 8]-NRT-code), using
- digital (0, 3, 129)-net over F128, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, m and t.
Other Results with Identical Parameters
None.
Depending Results
None.