Best Known (84−64, 84, s)-Nets in Base 64
(84−64, 84, 177)-Net over F64 — Constructive and digital
Digital (20, 84, 177)-net over F64, using
- t-expansion [i] based on digital (7, 84, 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
(84−64, 84, 216)-Net in Base 64 — Constructive
(20, 84, 216)-net in base 64, using
- t-expansion [i] based on (18, 84, 216)-net in base 64, using
- 7 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
- 7 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
(84−64, 84, 342)-Net over F64 — Digital
Digital (20, 84, 342)-net over F64, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 20 and N(F) ≥ 342, using
(84−64, 84, 11172)-Net in Base 64 — Upper bound on s
There is no (20, 84, 11173)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 52 486889 659327 584126 579806 229727 369524 261640 050441 226285 160388 637395 711747 211931 181822 092916 453408 139904 380587 095831 171649 304994 258300 808944 363858 334061 > 6484 [i]