Best Known (83−57, 83, s)-Nets in Base 64
(83−57, 83, 177)-Net over F64 — Constructive and digital
Digital (26, 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
(83−57, 83, 288)-Net in Base 64 — Constructive
(26, 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
(83−57, 83, 425)-Net over F64 — Digital
Digital (26, 83, 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
(83−57, 83, 34915)-Net in Base 64 — Upper bound on s
There is no (26, 83, 34916)-net in base 64, because
- 1 times m-reduction [i] would yield (26, 82, 34916)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 12791 905242 981947 907614 171987 412873 169641 191939 016730 055177 245170 783023 948181 882463 208184 815106 499003 923760 819407 196037 031385 391283 538362 027108 169048 > 6482 [i]