Best Known (72−52, 72, s)-Nets in Base 64
(72−52, 72, 177)-Net over F64 — Constructive and digital
Digital (20, 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
(72−52, 72, 288)-Net in Base 64 — Constructive
(20, 72, 288)-net in base 64, using
- 5 times m-reduction [i] based on (20, 77, 288)-net in base 64, using
- base change [i] based on digital (9, 66, 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, 66, 288)-net over F128, using
(72−52, 72, 342)-Net over F64 — Digital
Digital (20, 72, 342)-net over F64, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 20 and N(F) ≥ 342, using
(72−52, 72, 16801)-Net in Base 64 — Upper bound on s
There is no (20, 72, 16802)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 11099 258453 486737 300746 881314 447646 939170 231967 930488 409590 379508 547847 797918 942903 735635 875979 498994 057396 177450 128755 475302 665840 > 6472 [i]