Best Known (26, 26+14, s)-Nets in Base 128
(26, 26+14, 299593)-Net over F128 — Constructive and digital
Digital (26, 40, 299593)-net over F128, using
- net defined by OOA [i] based on linear OOA(12840, 299593, F128, 14, 14) (dual of [(299593, 14), 4194262, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(12840, 2097151, F128, 14) (dual of [2097151, 2097111, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(12840, 2097152, F128, 14) (dual of [2097152, 2097112, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(12840, 2097152, F128, 14) (dual of [2097152, 2097112, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(12840, 2097151, F128, 14) (dual of [2097151, 2097111, 15]-code), using
(26, 26+14, 735632)-Net over F128 — Digital
Digital (26, 40, 735632)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12840, 735632, F128, 2, 14) (dual of [(735632, 2), 1471224, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12840, 1048577, F128, 2, 14) (dual of [(1048577, 2), 2097114, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12840, 2097154, F128, 14) (dual of [2097154, 2097114, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(12840, 2097155, F128, 14) (dual of [2097155, 2097115, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(12840, 2097152, F128, 14) (dual of [2097152, 2097112, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(12837, 2097152, F128, 13) (dual of [2097152, 2097115, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(12840, 2097155, F128, 14) (dual of [2097155, 2097115, 15]-code), using
- OOA 2-folding [i] based on linear OA(12840, 2097154, F128, 14) (dual of [2097154, 2097114, 15]-code), using
- discarding factors / shortening the dual code based on linear OOA(12840, 1048577, F128, 2, 14) (dual of [(1048577, 2), 2097114, 15]-NRT-code), using
(26, 26+14, large)-Net in Base 128 — Upper bound on s
There is no (26, 40, large)-net in base 128, because
- 12 times m-reduction [i] would yield (26, 28, large)-net in base 128, but