Best Known (82−63, 82, s)-Nets in Base 64
(82−63, 82, 177)-Net over F64 — Constructive and digital
Digital (19, 82, 177)-net over F64, using
- t-expansion [i] based on digital (7, 82, 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
(82−63, 82, 216)-Net in Base 64 — Constructive
(19, 82, 216)-net in base 64, using
- t-expansion [i] based on (18, 82, 216)-net in base 64, using
- 9 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
- 9 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
(82−63, 82, 315)-Net over F64 — Digital
Digital (19, 82, 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
(82−63, 82, 10313)-Net in Base 64 — Upper bound on s
There is no (19, 82, 10314)-net in base 64, because
- 1 times m-reduction [i] would yield (19, 81, 10314)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 199 975700 676970 303311 137163 194118 741746 939187 039536 283488 281853 861791 550000 007385 221106 832676 958238 919177 742336 126002 932289 446549 492411 048816 379040 > 6481 [i]