Best Known (25−8, 25, s)-Nets in Base 128
(25−8, 25, 524291)-Net over F128 — Constructive and digital
Digital (17, 25, 524291)-net over F128, using
- net defined by OOA [i] based on linear OOA(12825, 524291, F128, 8, 8) (dual of [(524291, 8), 4194303, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(12825, 2097164, F128, 8) (dual of [2097164, 2097139, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(12825, 2097167, F128, 8) (dual of [2097167, 2097142, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(3) [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(12810, 2097152, F128, 4) (dual of [2097152, 2097142, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(1283, 15, F128, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,128) or 15-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(7) ⊂ Ce(3) [i] based on
- discarding factors / shortening the dual code based on linear OA(12825, 2097167, F128, 8) (dual of [2097167, 2097142, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(12825, 2097164, F128, 8) (dual of [2097164, 2097139, 9]-code), using
(25−8, 25, 2097167)-Net over F128 — Digital
Digital (17, 25, 2097167)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12825, 2097167, F128, 8) (dual of [2097167, 2097142, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(3) [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(12810, 2097152, F128, 4) (dual of [2097152, 2097142, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(1283, 15, F128, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,128) or 15-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(7) ⊂ Ce(3) [i] based on
(25−8, 25, large)-Net in Base 128 — Upper bound on s
There is no (17, 25, large)-net in base 128, because
- 6 times m-reduction [i] would yield (17, 19, large)-net in base 128, but