Best Known (67−57, 67, s)-Nets in Base 81
(67−57, 67, 172)-Net over F81 — Constructive and digital
Digital (10, 67, 172)-net over F81, using
- t-expansion [i] based on digital (7, 67, 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
(67−57, 67, 244)-Net over F81 — Digital
Digital (10, 67, 244)-net over F81, using
- t-expansion [i] based on digital (9, 67, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
(67−57, 67, 4437)-Net in Base 81 — Upper bound on s
There is no (10, 67, 4438)-net in base 81, because
- 1 times m-reduction [i] would yield (10, 66, 4438)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 915146 253673 587964 554440 013225 066562 424268 466247 867072 111245 858709 988829 485315 867866 400602 575727 396020 896631 423365 004091 208321 > 8166 [i]