Best Known (87−32, 87, s)-Nets in Base 64
(87−32, 87, 690)-Net over F64 — Constructive and digital
Digital (55, 87, 690)-net over F64, using
- t-expansion [i] based on digital (53, 87, 690)-net over F64, using
- 2 times m-reduction [i] based on digital (53, 89, 690)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (7, 25, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- digital (28, 64, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- digital (7, 25, 177)-net over F64, using
- (u, u+v)-construction [i] based on
- 2 times m-reduction [i] based on digital (53, 89, 690)-net over F64, using
(87−32, 87, 4096)-Net in Base 64 — Constructive
(55, 87, 4096)-net in base 64, using
- 1 times m-reduction [i] based on (55, 88, 4096)-net in base 64, using
- base change [i] based on digital (33, 66, 4096)-net over F256, using
- 2561 times duplication [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
- 2561 times duplication [i] based on digital (32, 65, 4096)-net over F256, using
- base change [i] based on digital (33, 66, 4096)-net over F256, using
(87−32, 87, 23117)-Net over F64 — Digital
Digital (55, 87, 23117)-net over F64, using
(87−32, 87, large)-Net in Base 64 — Upper bound on s
There is no (55, 87, large)-net in base 64, because
- 30 times m-reduction [i] would yield (55, 57, large)-net in base 64, but