Best Known (71−56, 71, s)-Nets in Base 64
(71−56, 71, 177)-Net over F64 — Constructive and digital
Digital (15, 71, 177)-net over F64, using
- t-expansion [i] based on digital (7, 71, 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
(71−56, 71, 192)-Net in Base 64 — Constructive
(15, 71, 192)-net in base 64, using
- 13 times m-reduction [i] based on (15, 84, 192)-net in base 64, using
- base change [i] based on digital (3, 72, 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, 72, 192)-net over F128, using
(71−56, 71, 258)-Net over F64 — Digital
Digital (15, 71, 258)-net over F64, using
- net from sequence [i] based on digital (15, 257)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 15 and N(F) ≥ 258, using
(71−56, 71, 6803)-Net in Base 64 — Upper bound on s
There is no (15, 71, 6804)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 173 652588 661620 538843 835559 911221 365428 445495 819970 032056 046835 121356 528321 572857 634738 446225 907208 233859 266641 330818 860894 238240 > 6471 [i]