Information on Result #1210169
Digital (168, 180, 5941933)-net over F4, using (u, u+v)-construction based on
- digital (38, 44, 349533)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 5)-net over F4, using
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 0 and N(F) ≥ 5, using
- the rational function field F4(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- digital (35, 41, 349528)-net over F4, using
- net defined by OOA [i] based on linear OOA(441, 349528, F4, 6, 6) (dual of [(349528, 6), 2097127, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(441, 1048584, F4, 6) (dual of [1048584, 1048543, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(441, 1048586, F4, 6) (dual of [1048586, 1048545, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(441, 1048576, F4, 6) (dual of [1048576, 1048535, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(431, 1048576, F4, 5) (dual of [1048576, 1048545, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(40, 10, F4, 0) (dual of [10, 10, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(441, 1048586, F4, 6) (dual of [1048586, 1048545, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(441, 1048584, F4, 6) (dual of [1048584, 1048543, 7]-code), using
- net defined by OOA [i] based on linear OOA(441, 349528, F4, 6, 6) (dual of [(349528, 6), 2097127, 7]-NRT-code), using
- digital (0, 3, 5)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (124, 136, 5592400)-net over F4, using
- trace code for nets [i] based on digital (56, 68, 2796200)-net over F16, using
- net defined by OOA [i] based on linear OOA(1668, 2796200, F16, 14, 12) (dual of [(2796200, 14), 39146732, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(1668, 8388601, F16, 2, 12) (dual of [(8388601, 2), 16777134, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1668, 8388602, F16, 2, 12) (dual of [(8388602, 2), 16777136, 13]-NRT-code), using
- trace code [i] based on linear OOA(25634, 4194301, F256, 2, 12) (dual of [(4194301, 2), 8388568, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25634, 8388602, F256, 12) (dual of [8388602, 8388568, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- OOA 2-folding [i] based on linear OA(25634, 8388602, F256, 12) (dual of [8388602, 8388568, 13]-code), using
- trace code [i] based on linear OOA(25634, 4194301, F256, 2, 12) (dual of [(4194301, 2), 8388568, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1668, 8388602, F16, 2, 12) (dual of [(8388602, 2), 16777136, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(1668, 8388601, F16, 2, 12) (dual of [(8388601, 2), 16777134, 13]-NRT-code), using
- net defined by OOA [i] based on linear OOA(1668, 2796200, F16, 14, 12) (dual of [(2796200, 14), 39146732, 13]-NRT-code), using
- trace code for nets [i] based on digital (56, 68, 2796200)-net over F16, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.