Best Known (85−59, 85, s)-Nets in Base 64
(85−59, 85, 177)-Net over F64 — Constructive and digital
Digital (26, 85, 177)-net over F64, using
- t-expansion [i] based on digital (7, 85, 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
(85−59, 85, 288)-Net in Base 64 — Constructive
(26, 85, 288)-net in base 64, using
- t-expansion [i] based on (22, 85, 288)-net in base 64, using
- 6 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
- 6 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(85−59, 85, 425)-Net over F64 — Digital
Digital (26, 85, 425)-net over F64, using
- net from sequence [i] based on digital (26, 424)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 26 and N(F) ≥ 425, using
(85−59, 85, 31570)-Net in Base 64 — Upper bound on s
There is no (26, 85, 31571)-net in base 64, because
- 1 times m-reduction [i] would yield (26, 84, 31571)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 52 416219 656694 481461 254184 483178 463075 772491 956205 148720 361112 812934 576369 582377 030059 051066 526212 469483 347296 736475 752653 672385 487080 969910 846240 080160 > 6484 [i]