Best Known (33−8, 33, s)-Nets in Base 128
(33−8, 33, 2097279)-Net over F128 — Constructive and digital
Digital (25, 33, 2097279)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 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
- 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
- digital (0, 4, 129)-net over F128, using
(33−8, 33, 2129790)-Net in Base 128 — Constructive
(25, 33, 2129790)-net in base 128, using
- 1281 times duplication [i] based on (24, 32, 2129790)-net in base 128, using
- base change [i] based on digital (20, 28, 2129790)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (2, 6, 32640)-net over F256, using
- net defined by OOA [i] based on linear OOA(2566, 32640, F256, 4, 4) (dual of [(32640, 4), 130554, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(2566, 65280, F256, 4) (dual of [65280, 65274, 5]-code), using
- 1 times truncation [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(2566, 65280, F256, 4) (dual of [65280, 65274, 5]-code), using
- net defined by OOA [i] based on linear OOA(2566, 32640, F256, 4, 4) (dual of [(32640, 4), 130554, 5]-NRT-code), using
- digital (14, 22, 2097150)-net over F256, using
- net defined by OOA [i] based on linear OOA(25622, 2097150, F256, 8, 8) (dual of [(2097150, 8), 16777178, 9]-NRT-code), using
- OA 4-folding and stacking [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
- OA 4-folding and stacking [i] based on linear OA(25622, 8388600, F256, 8) (dual of [8388600, 8388578, 9]-code), using
- net defined by OOA [i] based on linear OOA(25622, 2097150, F256, 8, 8) (dual of [(2097150, 8), 16777178, 9]-NRT-code), using
- digital (2, 6, 32640)-net over F256, using
- (u, u+v)-construction [i] based on
- base change [i] based on digital (20, 28, 2129790)-net over F256, using
(33−8, 33, large)-Net over F128 — Digital
Digital (25, 33, large)-net over F128, using
- t-expansion [i] based on digital (24, 33, large)-net over F128, using
(33−8, 33, large)-Net in Base 128 — Upper bound on s
There is no (25, 33, large)-net in base 128, because
- 6 times m-reduction [i] would yield (25, 27, large)-net in base 128, but