Best Known (12, 12+59, s)-Nets in Base 81
(12, 12+59, 172)-Net over F81 — Constructive and digital
Digital (12, 71, 172)-net over F81, using
- t-expansion [i] based on digital (7, 71, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
(12, 12+59, 298)-Net over F81 — Digital
Digital (12, 71, 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
(12, 12+59, 5883)-Net in Base 81 — Upper bound on s
There is no (12, 71, 5884)-net in base 81, because
- 1 times m-reduction [i] would yield (12, 70, 5884)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 39 288785 938928 552393 737580 339775 919024 713319 039587 696157 872575 485109 507968 222664 719640 107510 724693 608903 561241 354901 690928 078674 898881 > 8170 [i]