Best Known (20, 30, s)-Nets in Base 128
(20, 30, 419432)-Net over F128 — Constructive and digital
Digital (20, 30, 419432)-net over F128, using
- net defined by OOA [i] based on linear OOA(12830, 419432, F128, 10, 10) (dual of [(419432, 10), 4194290, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(12830, 2097160, F128, 10) (dual of [2097160, 2097130, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(12830, 2097163, F128, 10) (dual of [2097163, 2097133, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- linear OA(12828, 2097152, F128, 10) (dual of [2097152, 2097124, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(1282, 11, F128, 2) (dual of [11, 9, 3]-code or 11-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(9) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(12830, 2097163, F128, 10) (dual of [2097163, 2097133, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(12830, 2097160, F128, 10) (dual of [2097160, 2097130, 11]-code), using
(20, 30, 1289797)-Net over F128 — Digital
Digital (20, 30, 1289797)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12830, 1289797, F128, 10) (dual of [1289797, 1289767, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(12830, 2097163, F128, 10) (dual of [2097163, 2097133, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- linear OA(12828, 2097152, F128, 10) (dual of [2097152, 2097124, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(1282, 11, F128, 2) (dual of [11, 9, 3]-code or 11-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(9) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(12830, 2097163, F128, 10) (dual of [2097163, 2097133, 11]-code), using
(20, 30, large)-Net in Base 128 — Upper bound on s
There is no (20, 30, large)-net in base 128, because
- 8 times m-reduction [i] would yield (20, 22, large)-net in base 128, but