Best Known (63−16, 63, s)-Nets in Base 128
(63−16, 63, 1048575)-Net over F128 — Constructive and digital
Digital (47, 63, 1048575)-net over F128, using
- 1282 times duplication [i] based on digital (45, 61, 1048575)-net over F128, using
- net defined by OOA [i] based on linear OOA(12861, 1048575, F128, 16, 16) (dual of [(1048575, 16), 16777139, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(12861, 8388600, F128, 16) (dual of [8388600, 8388539, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(12861, large, F128, 16) (dual of [large, large−61, 17]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9256395 | 1284−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(12861, large, F128, 16) (dual of [large, large−61, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(12861, 8388600, F128, 16) (dual of [8388600, 8388539, 17]-code), using
- net defined by OOA [i] based on linear OOA(12861, 1048575, F128, 16, 16) (dual of [(1048575, 16), 16777139, 17]-NRT-code), using
(63−16, 63, 1048832)-Net in Base 128 — Constructive
(47, 63, 1048832)-net in base 128, using
- (u, u+v)-construction [i] based on
- (2, 10, 257)-net in base 128, using
- 6 times m-reduction [i] based on (2, 16, 257)-net in base 128, using
- base change [i] based on digital (0, 14, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 14, 257)-net over F256, using
- 6 times m-reduction [i] based on (2, 16, 257)-net in base 128, using
- (37, 53, 1048575)-net in base 128, using
- net defined by OOA [i] based on OOA(12853, 1048575, S128, 16, 16), using
- OA 8-folding and stacking [i] based on OA(12853, 8388600, S128, 16), using
- discarding factors based on OA(12853, large, S128, 16), using
- discarding parts of the base [i] based on linear OA(25646, large, F256, 16) (dual of [large, large−46, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding parts of the base [i] based on linear OA(25646, large, F256, 16) (dual of [large, large−46, 17]-code), using
- discarding factors based on OA(12853, large, S128, 16), using
- OA 8-folding and stacking [i] based on OA(12853, 8388600, S128, 16), using
- net defined by OOA [i] based on OOA(12853, 1048575, S128, 16, 16), using
- (2, 10, 257)-net in base 128, using
(63−16, 63, large)-Net over F128 — Digital
Digital (47, 63, large)-net over F128, using
- t-expansion [i] based on digital (46, 63, large)-net over F128, using
(63−16, 63, large)-Net in Base 128 — Upper bound on s
There is no (47, 63, large)-net in base 128, because
- 14 times m-reduction [i] would yield (47, 49, large)-net in base 128, but