Best Known (15, 23, s)-Nets in Base 128
(15, 23, 524289)-Net over F128 — Constructive and digital
Digital (15, 23, 524289)-net over F128, using
- net defined by OOA [i] based on linear OOA(12823, 524289, F128, 8, 8) (dual of [(524289, 8), 4194289, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(12823, 2097156, F128, 8) (dual of [2097156, 2097133, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(12823, 2097159, F128, 8) (dual of [2097159, 2097136, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(12822, 2097152, F128, 8) (dual of [2097152, 2097130, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(12816, 2097152, F128, 6) (dual of [2097152, 2097136, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(12823, 2097159, F128, 8) (dual of [2097159, 2097136, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(12823, 2097156, F128, 8) (dual of [2097156, 2097133, 9]-code), using
(15, 23, 1255608)-Net over F128 — Digital
Digital (15, 23, 1255608)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12823, 1255608, F128, 8) (dual of [1255608, 1255585, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(12823, 2097159, F128, 8) (dual of [2097159, 2097136, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(12822, 2097152, F128, 8) (dual of [2097152, 2097130, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(12816, 2097152, F128, 6) (dual of [2097152, 2097136, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(12823, 2097159, F128, 8) (dual of [2097159, 2097136, 9]-code), using
(15, 23, large)-Net in Base 128 — Upper bound on s
There is no (15, 23, large)-net in base 128, because
- 6 times m-reduction [i] would yield (15, 17, large)-net in base 128, but