Best Known (86−70, 86, s)-Nets in Base 64
(86−70, 86, 177)-Net over F64 — Constructive and digital
Digital (16, 86, 177)-net over F64, using
- t-expansion [i] based on digital (7, 86, 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
(86−70, 86, 192)-Net in Base 64 — Constructive
(16, 86, 192)-net in base 64, using
- 5 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
(86−70, 86, 267)-Net over F64 — Digital
Digital (16, 86, 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
(86−70, 86, 6035)-Net in Base 64 — Upper bound on s
There is no (16, 86, 6036)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 215293 090007 019433 125656 745699 270399 376441 056650 849032 100363 335712 068771 482132 315014 542655 492251 628214 845381 658676 794578 351749 571607 427994 071686 195697 912276 > 6486 [i]