Best Known (31−8, 31, s)-Nets in Base 128
(31−8, 31, 2097150)-Net over F128 — Constructive and digital
Digital (23, 31, 2097150)-net over F128, using
- 1282 times duplication [i] based on digital (21, 29, 2097150)-net over F128, using
- net defined by OOA [i] based on linear OOA(12829, 2097150, F128, 8, 8) (dual of [(2097150, 8), 16777171, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(12829, 8388600, F128, 8) (dual of [8388600, 8388571, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(12829, large, F128, 8) (dual of [large, large−29, 9]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 17895697 | 1284−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(12829, large, F128, 8) (dual of [large, large−29, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(12829, 8388600, F128, 8) (dual of [8388600, 8388571, 9]-code), using
- net defined by OOA [i] based on linear OOA(12829, 2097150, F128, 8, 8) (dual of [(2097150, 8), 16777171, 9]-NRT-code), using
(31−8, 31, 2097407)-Net in Base 128 — Constructive
(23, 31, 2097407)-net in base 128, using
- net defined by OOA [i] based on OOA(12831, 2097407, S128, 12, 8), using
- OOA stacking with additional row [i] based on OOA(12831, 2097408, S128, 4, 8), using
- discarding parts of the base [i] based on linear OOA(25627, 2097408, F256, 4, 8) (dual of [(2097408, 4), 8389605, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2565, 258, F256, 4, 4) (dual of [(258, 4), 1027, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(2565, 258, F256, 3, 4) (dual of [(258, 3), 769, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 5, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- extracting embedded OOA [i] based on digital (1, 5, 258)-net over F256, using
- appending kth column [i] based on linear OOA(2565, 258, F256, 3, 4) (dual of [(258, 3), 769, 5]-NRT-code), using
- linear OOA(25622, 2097150, F256, 4, 8) (dual of [(2097150, 4), 8388578, 9]-NRT-code), using
- OOA 4-folding [i] based on linear OA(25622, 8388600, F256, 8) (dual of [8388600, 8388578, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(25622, large, F256, 8) (dual of [large, large−22, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(25622, large, F256, 8) (dual of [large, large−22, 9]-code), using
- OOA 4-folding [i] based on linear OA(25622, 8388600, F256, 8) (dual of [8388600, 8388578, 9]-code), using
- linear OOA(2565, 258, F256, 4, 4) (dual of [(258, 4), 1027, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding parts of the base [i] based on linear OOA(25627, 2097408, F256, 4, 8) (dual of [(2097408, 4), 8389605, 9]-NRT-code), using
- OOA stacking with additional row [i] based on OOA(12831, 2097408, S128, 4, 8), using
(31−8, 31, large)-Net over F128 — Digital
Digital (23, 31, large)-net over F128, using
- 1282 times duplication [i] based on digital (21, 29, large)-net over F128, using
(31−8, 31, large)-Net in Base 128 — Upper bound on s
There is no (23, 31, large)-net in base 128, because
- 6 times m-reduction [i] would yield (23, 25, large)-net in base 128, but