Best Known (39, 39+14, s)-Nets in Base 128
(39, 39+14, 1198371)-Net over F128 — Constructive and digital
Digital (39, 53, 1198371)-net over F128, using
- net defined by OOA [i] based on linear OOA(12853, 1198371, F128, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(12853, 8388597, F128, 14) (dual of [8388597, 8388544, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(12853, large, F128, 14) (dual of [large, large−53, 15]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9256395 | 1284−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(12853, large, F128, 14) (dual of [large, large−53, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(12853, 8388597, F128, 14) (dual of [8388597, 8388544, 15]-code), using
(39, 39+14, 1198500)-Net in Base 128 — Constructive
(39, 53, 1198500)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- (32, 46, 1198371)-net in base 128, using
- net defined by OOA [i] based on OOA(12846, 1198371, S128, 14, 14), using
- OA 7-folding and stacking [i] based on OA(12846, 8388597, S128, 14), using
- discarding factors based on OA(12846, large, S128, 14), using
- discarding parts of the base [i] based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding parts of the base [i] based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- discarding factors based on OA(12846, large, S128, 14), using
- OA 7-folding and stacking [i] based on OA(12846, 8388597, S128, 14), using
- net defined by OOA [i] based on OOA(12846, 1198371, S128, 14, 14), using
- digital (0, 7, 129)-net over F128, using
(39, 39+14, large)-Net over F128 — Digital
Digital (39, 53, large)-net over F128, using
- 1281 times duplication [i] based on digital (38, 52, large)-net over F128, using
(39, 39+14, large)-Net in Base 128 — Upper bound on s
There is no (39, 53, large)-net in base 128, because
- 12 times m-reduction [i] would yield (39, 41, large)-net in base 128, but