Best Known (26, 50, s)-Nets in Base 128
(26, 50, 1366)-Net over F128 — Constructive and digital
Digital (26, 50, 1366)-net over F128, using
- 1281 times duplication [i] based on digital (25, 49, 1366)-net over F128, using
- net defined by OOA [i] based on linear OOA(12849, 1366, F128, 24, 24) (dual of [(1366, 24), 32735, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(12849, 16392, F128, 24) (dual of [16392, 16343, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- linear OA(12847, 16384, F128, 24) (dual of [16384, 16337, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(12841, 16384, F128, 21) (dual of [16384, 16343, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(1282, 8, F128, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- OA 12-folding and stacking [i] based on linear OA(12849, 16392, F128, 24) (dual of [16392, 16343, 25]-code), using
- net defined by OOA [i] based on linear OOA(12849, 1366, F128, 24, 24) (dual of [(1366, 24), 32735, 25]-NRT-code), using
(26, 50, 5465)-Net over F128 — Digital
Digital (26, 50, 5465)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12850, 5465, F128, 3, 24) (dual of [(5465, 3), 16345, 25]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12850, 16395, F128, 24) (dual of [16395, 16345, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(19) [i] based on
- linear OA(12847, 16384, F128, 24) (dual of [16384, 16337, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(12839, 16384, F128, 20) (dual of [16384, 16345, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1283, 11, F128, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,128) or 11-cap in PG(2,128)), using
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- Reed–Solomon code RS(125,128) [i]
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- construction X applied to Ce(23) ⊂ Ce(19) [i] based on
- OOA 3-folding [i] based on linear OA(12850, 16395, F128, 24) (dual of [16395, 16345, 25]-code), using
(26, 50, large)-Net in Base 128 — Upper bound on s
There is no (26, 50, large)-net in base 128, because
- 22 times m-reduction [i] would yield (26, 28, large)-net in base 128, but