Best Known (83−67, 83, s)-Nets in Base 64
(83−67, 83, 177)-Net over F64 — Constructive and digital
Digital (16, 83, 177)-net over F64, using
- t-expansion [i] based on digital (7, 83, 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
(83−67, 83, 192)-Net in Base 64 — Constructive
(16, 83, 192)-net in base 64, using
- 8 times m-reduction [i] based on (16, 91, 192)-net in base 64, using
- base change [i] based on digital (3, 78, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 78, 192)-net over F128, using
(83−67, 83, 267)-Net over F64 — Digital
Digital (16, 83, 267)-net over F64, using
- net from sequence [i] based on digital (16, 266)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 16 and N(F) ≥ 267, using
(83−67, 83, 6411)-Net in Base 64 — Upper bound on s
There is no (16, 83, 6412)-net in base 64, because
- 1 times m-reduction [i] would yield (16, 82, 6412)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 12799 860856 896916 006462 652430 361160 706042 932413 449577 493277 329056 629186 642463 728217 332605 123118 594960 071829 414940 667454 670499 893278 044786 531667 866680 > 6482 [i]