Best Known (19, 19+64, s)-Nets in Base 64
(19, 19+64, 177)-Net over F64 — Constructive and digital
Digital (19, 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
(19, 19+64, 216)-Net in Base 64 — Constructive
(19, 83, 216)-net in base 64, using
- t-expansion [i] based on (18, 83, 216)-net in base 64, using
- 8 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
- base change [i] based on digital (5, 78, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- base change [i] based on digital (5, 78, 216)-net over F128, using
- 8 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
(19, 19+64, 315)-Net over F64 — Digital
Digital (19, 83, 315)-net over F64, using
- net from sequence [i] based on digital (19, 314)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 19 and N(F) ≥ 315, using
(19, 19+64, 9808)-Net in Base 64 — Upper bound on s
There is no (19, 83, 9809)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 819165 520598 311571 407789 268963 906569 604211 483593 102148 986063 333145 348798 203372 207463 342380 940038 113889 267355 344333 491944 799039 091726 372711 668559 531650 > 6483 [i]