Best Known (83−58, 83, s)-Nets in Base 64
(83−58, 83, 177)-Net over F64 — Constructive and digital
Digital (25, 83, 177)-net over F64, using
- t-expansion [i] based on digital (7, 83, 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
(83−58, 83, 288)-Net in Base 64 — Constructive
(25, 83, 288)-net in base 64, using
- t-expansion [i] based on (22, 83, 288)-net in base 64, using
- 8 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
- 8 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(83−58, 83, 408)-Net over F64 — Digital
Digital (25, 83, 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
(83−58, 83, 27350)-Net in Base 64 — Upper bound on s
There is no (25, 83, 27351)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 818872 700843 141195 743443 004277 285569 557803 678767 829940 086781 253646 461703 407356 593870 310105 777609 734819 770560 517585 438862 225515 069877 945579 113824 248656 > 6483 [i]