Best Known (82−67, 82, s)-Nets in Base 81
(82−67, 82, 224)-Net over F81 — Constructive and digital
Digital (15, 82, 224)-net over F81, using
- t-expansion [i] based on digital (13, 82, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
(82−67, 82, 298)-Net over F81 — Digital
Digital (15, 82, 298)-net over F81, using
- t-expansion [i] based on digital (12, 82, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
(82−67, 82, 7940)-Net in Base 81 — Upper bound on s
There is no (15, 82, 7941)-net in base 81, because
- 1 times m-reduction [i] would yield (15, 81, 7941)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 38792 152832 146430 703841 747704 097016 155795 244092 939818 174184 322275 017308 373584 424498 986649 274889 866685 434554 134794 662754 029627 855325 226521 856156 592450 327441 > 8181 [i]