Best Known (19, 19+66, s)-Nets in Base 64
(19, 19+66, 177)-Net over F64 — Constructive and digital
Digital (19, 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
(19, 19+66, 216)-Net in Base 64 — Constructive
(19, 85, 216)-net in base 64, using
- t-expansion [i] based on (18, 85, 216)-net in base 64, using
- 6 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
- 6 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
(19, 19+66, 315)-Net over F64 — Digital
Digital (19, 85, 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+66, 9365)-Net in Base 64 — Upper bound on s
There is no (19, 85, 9366)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 3358 094866 389871 252124 735232 685555 855919 490385 897396 343168 290679 640088 210130 529914 107962 705876 291023 906069 537301 379709 950579 762419 477386 362097 210996 900092 > 6485 [i]