Best Known (88−62, 88, s)-Nets in Base 64
(88−62, 88, 177)-Net over F64 — Constructive and digital
Digital (26, 88, 177)-net over F64, using
- t-expansion [i] based on digital (7, 88, 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
(88−62, 88, 288)-Net in Base 64 — Constructive
(26, 88, 288)-net in base 64, using
- t-expansion [i] based on (22, 88, 288)-net in base 64, using
- 3 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
- 3 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(88−62, 88, 425)-Net over F64 — Digital
Digital (26, 88, 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
(88−62, 88, 26403)-Net in Base 64 — Upper bound on s
There is no (26, 88, 26404)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 879 412678 515866 575072 485100 326475 449439 566488 024012 792146 331220 169844 749272 885918 481116 549644 413390 303372 057295 659469 586298 171765 755164 513158 602501 059389 902904 > 6488 [i]