Best Known (26, 26+12, s)-Nets in Base 128
(26, 26+12, 349528)-Net over F128 — Constructive and digital
Digital (26, 38, 349528)-net over F128, using
- net defined by OOA [i] based on linear OOA(12838, 349528, F128, 12, 12) (dual of [(349528, 12), 4194298, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(12838, 2097168, F128, 12) (dual of [2097168, 2097130, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(12838, 2097171, F128, 12) (dual of [2097171, 2097133, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(6) [i] based on
- linear OA(12834, 2097152, F128, 12) (dual of [2097152, 2097118, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(12819, 2097152, F128, 7) (dual of [2097152, 2097133, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(1284, 19, F128, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,128)), using
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- Reed–Solomon code RS(124,128) [i]
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- construction X applied to Ce(11) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(12838, 2097171, F128, 12) (dual of [2097171, 2097133, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(12838, 2097168, F128, 12) (dual of [2097168, 2097130, 13]-code), using
(26, 26+12, 2097171)-Net over F128 — Digital
Digital (26, 38, 2097171)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12838, 2097171, F128, 12) (dual of [2097171, 2097133, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(6) [i] based on
- linear OA(12834, 2097152, F128, 12) (dual of [2097152, 2097118, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(12819, 2097152, F128, 7) (dual of [2097152, 2097133, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(1284, 19, F128, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,128)), using
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- Reed–Solomon code RS(124,128) [i]
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- construction X applied to Ce(11) ⊂ Ce(6) [i] based on
(26, 26+12, large)-Net in Base 128 — Upper bound on s
There is no (26, 38, large)-net in base 128, because
- 10 times m-reduction [i] would yield (26, 28, large)-net in base 128, but