Best Known (77−61, 77, s)-Nets in Base 64
(77−61, 77, 177)-Net over F64 — Constructive and digital
Digital (16, 77, 177)-net over F64, using
- t-expansion [i] based on digital (7, 77, 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
(77−61, 77, 216)-Net in Base 64 — Constructive
(16, 77, 216)-net in base 64, using
- base change [i] based on digital (5, 66, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
(77−61, 77, 267)-Net over F64 — Digital
Digital (16, 77, 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
(77−61, 77, 7181)-Net in Base 64 — Upper bound on s
There is no (16, 77, 7182)-net in base 64, because
- 1 times m-reduction [i] would yield (16, 76, 7182)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 186658 255333 570733 594278 551986 104838 114576 083776 789368 287031 177280 070473 819408 174783 641251 230181 774192 192904 031309 605776 975055 532370 531840 > 6476 [i]