Best Known (41, 67, s)-Nets in Base 128
(41, 67, 1452)-Net over F128 — Constructive and digital
Digital (41, 67, 1452)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 16, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- digital (25, 51, 1260)-net over F128, using
- net defined by OOA [i] based on linear OOA(12851, 1260, F128, 26, 26) (dual of [(1260, 26), 32709, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(12851, 16380, F128, 26) (dual of [16380, 16329, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(12851, 16384, F128, 26) (dual of [16384, 16333, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(12851, 16384, F128, 26) (dual of [16384, 16333, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(12851, 16380, F128, 26) (dual of [16380, 16329, 27]-code), using
- net defined by OOA [i] based on linear OOA(12851, 1260, F128, 26, 26) (dual of [(1260, 26), 32709, 27]-NRT-code), using
- digital (3, 16, 192)-net over F128, using
(41, 67, 5043)-Net in Base 128 — Constructive
(41, 67, 5043)-net in base 128, using
- net defined by OOA [i] based on OOA(12867, 5043, S128, 26, 26), using
- OA 13-folding and stacking [i] based on OA(12867, 65559, S128, 26), using
- discarding parts of the base [i] based on linear OA(25658, 65559, F256, 26) (dual of [65559, 65501, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(17) [i] based on
- linear OA(25651, 65536, F256, 26) (dual of [65536, 65485, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2567, 23, F256, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,256)), using
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
- Reed–Solomon code RS(249,256) [i]
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
- construction X applied to Ce(25) ⊂ Ce(17) [i] based on
- discarding parts of the base [i] based on linear OA(25658, 65559, F256, 26) (dual of [65559, 65501, 27]-code), using
- OA 13-folding and stacking [i] based on OA(12867, 65559, S128, 26), using
(41, 67, 35587)-Net over F128 — Digital
Digital (41, 67, 35587)-net over F128, using
(41, 67, large)-Net in Base 128 — Upper bound on s
There is no (41, 67, large)-net in base 128, because
- 24 times m-reduction [i] would yield (41, 43, large)-net in base 128, but