Information on Result #1217453
Digital (110, 123, 2800585)-net over F9, using (u, u+v)-construction based on
- digital (19, 25, 4385)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 10)-net over F9, using
- net from sequence [i] based on digital (0, 9)-sequence over F9, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 0 and N(F) ≥ 10, using
- the rational function field F9(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 9)-sequence over F9, using
- digital (16, 22, 4375)-net over F9, using
- net defined by OOA [i] based on linear OOA(922, 4375, F9, 6, 6) (dual of [(4375, 6), 26228, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(922, 13125, F9, 6) (dual of [13125, 13103, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(922, 13126, F9, 6) (dual of [13126, 13104, 7]-code), using
- trace code [i] based on linear OA(8111, 6563, F81, 6) (dual of [6563, 6552, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(8111, 6561, F81, 6) (dual of [6561, 6550, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(819, 6561, F81, 5) (dual of [6561, 6552, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- trace code [i] based on linear OA(8111, 6563, F81, 6) (dual of [6563, 6552, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(922, 13126, F9, 6) (dual of [13126, 13104, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(922, 13125, F9, 6) (dual of [13125, 13103, 7]-code), using
- net defined by OOA [i] based on linear OOA(922, 4375, F9, 6, 6) (dual of [(4375, 6), 26228, 7]-NRT-code), using
- digital (0, 3, 10)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (85, 98, 2796200)-net over F9, using
- net defined by OOA [i] based on linear OOA(998, 2796200, F9, 14, 13) (dual of [(2796200, 14), 39146702, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(998, 8388601, F9, 2, 13) (dual of [(8388601, 2), 16777104, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(998, 8388602, F9, 2, 13) (dual of [(8388602, 2), 16777106, 14]-NRT-code), using
- trace code [i] based on linear OOA(8149, 4194301, F81, 2, 13) (dual of [(4194301, 2), 8388553, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8149, 8388602, F81, 13) (dual of [8388602, 8388553, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(8149, large, F81, 13) (dual of [large, large−49, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8149, large, F81, 13) (dual of [large, large−49, 14]-code), using
- OOA 2-folding [i] based on linear OA(8149, 8388602, F81, 13) (dual of [8388602, 8388553, 14]-code), using
- trace code [i] based on linear OOA(8149, 4194301, F81, 2, 13) (dual of [(4194301, 2), 8388553, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(998, 8388602, F9, 2, 13) (dual of [(8388602, 2), 16777106, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(998, 8388601, F9, 2, 13) (dual of [(8388601, 2), 16777104, 14]-NRT-code), using
- net defined by OOA [i] based on linear OOA(998, 2796200, F9, 14, 13) (dual of [(2796200, 14), 39146702, 14]-NRT-code), 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.