Best Known (77, 110, s)-Nets in Base 32
(77, 110, 2080)-Net over F32 — Constructive and digital
Digital (77, 110, 2080)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 16, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- digital (61, 94, 2047)-net over F32, using
- net defined by OOA [i] based on linear OOA(3294, 2047, F32, 33, 33) (dual of [(2047, 33), 67457, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(3294, 32753, F32, 33) (dual of [32753, 32659, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(3294, 32768, F32, 33) (dual of [32768, 32674, 34]-code), using
- an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- discarding factors / shortening the dual code based on linear OA(3294, 32768, F32, 33) (dual of [32768, 32674, 34]-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(3294, 32753, F32, 33) (dual of [32753, 32659, 34]-code), using
- net defined by OOA [i] based on linear OOA(3294, 2047, F32, 33, 33) (dual of [(2047, 33), 67457, 34]-NRT-code), using
- digital (0, 16, 33)-net over F32, using
(77, 110, 4096)-Net in Base 32 — Constructive
(77, 110, 4096)-net in base 32, using
- 326 times duplication [i] based on (71, 104, 4096)-net in base 32, using
- base change [i] based on digital (32, 65, 4096)-net over F256, using
- net defined by OOA [i] based on linear OOA(25665, 4096, F256, 33, 33) (dual of [(4096, 33), 135103, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(25665, 65537, F256, 33) (dual of [65537, 65472, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- OOA 16-folding and stacking with additional row [i] based on linear OA(25665, 65537, F256, 33) (dual of [65537, 65472, 34]-code), using
- net defined by OOA [i] based on linear OOA(25665, 4096, F256, 33, 33) (dual of [(4096, 33), 135103, 34]-NRT-code), using
- base change [i] based on digital (32, 65, 4096)-net over F256, using
(77, 110, 61601)-Net over F32 — Digital
Digital (77, 110, 61601)-net over F32, using
(77, 110, large)-Net in Base 32 — Upper bound on s
There is no (77, 110, large)-net in base 32, because
- 31 times m-reduction [i] would yield (77, 79, large)-net in base 32, but