Best Known (90−65, 90, s)-Nets in Base 64
(90−65, 90, 177)-Net over F64 — Constructive and digital
Digital (25, 90, 177)-net over F64, using
- t-expansion [i] based on digital (7, 90, 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
(90−65, 90, 288)-Net in Base 64 — Constructive
(25, 90, 288)-net in base 64, using
- t-expansion [i] based on (22, 90, 288)-net in base 64, using
- 1 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
- 1 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(90−65, 90, 408)-Net over F64 — Digital
Digital (25, 90, 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
(90−65, 90, 21411)-Net in Base 64 — Upper bound on s
There is no (25, 90, 21412)-net in base 64, because
- 1 times m-reduction [i] would yield (25, 89, 21412)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 56252 503725 874967 885753 948797 657462 790992 463011 212241 378515 732131 323646 295642 955136 756712 621014 390544 512787 773291 304313 098469 320068 905207 760230 667031 365138 946565 > 6489 [i]