Best Known (30, 30+31, s)-Nets in Base 128
(30, 30+31, 1092)-Net over F128 — Constructive and digital
Digital (30, 61, 1092)-net over F128, using
- net defined by OOA [i] based on linear OOA(12861, 1092, F128, 31, 31) (dual of [(1092, 31), 33791, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(12861, 16381, F128, 31) (dual of [16381, 16320, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(12861, 16384, F128, 31) (dual of [16384, 16323, 32]-code), using
- an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- discarding factors / shortening the dual code based on linear OA(12861, 16384, F128, 31) (dual of [16384, 16323, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(12861, 16381, F128, 31) (dual of [16381, 16320, 32]-code), using
(30, 30+31, 3448)-Net over F128 — Digital
Digital (30, 61, 3448)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12861, 3448, F128, 4, 31) (dual of [(3448, 4), 13731, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12861, 4096, F128, 4, 31) (dual of [(4096, 4), 16323, 32]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12861, 16384, F128, 31) (dual of [16384, 16323, 32]-code), using
- an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- OOA 4-folding [i] based on linear OA(12861, 16384, F128, 31) (dual of [16384, 16323, 32]-code), using
- discarding factors / shortening the dual code based on linear OOA(12861, 4096, F128, 4, 31) (dual of [(4096, 4), 16323, 32]-NRT-code), using
(30, 30+31, large)-Net in Base 128 — Upper bound on s
There is no (30, 61, large)-net in base 128, because
- 29 times m-reduction [i] would yield (30, 32, large)-net in base 128, but