Best Known (72−47, 72, s)-Nets in Base 64
(72−47, 72, 177)-Net over F64 — Constructive and digital
Digital (25, 72, 177)-net over F64, using
- t-expansion [i] based on digital (7, 72, 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
(72−47, 72, 288)-Net in Base 64 — Constructive
(25, 72, 288)-net in base 64, using
- t-expansion [i] based on (22, 72, 288)-net in base 64, using
- 19 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- base change [i] based on digital (9, 78, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 78, 288)-net over F128, using
- 19 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(72−47, 72, 408)-Net over F64 — Digital
Digital (25, 72, 408)-net over F64, using
- net from sequence [i] based on digital (25, 407)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 25 and N(F) ≥ 408, using
(72−47, 72, 56315)-Net in Base 64 — Upper bound on s
There is no (25, 72, 56316)-net in base 64, because
- 1 times m-reduction [i] would yield (25, 71, 56316)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 173 334556 837101 856478 540379 550555 629405 136115 992534 636337 639456 862462 979749 469128 622751 604679 542664 039959 548653 940028 173060 874766 > 6471 [i]