Best Known (71−61, 71, s)-Nets in Base 81
(71−61, 71, 172)-Net over F81 — Constructive and digital
Digital (10, 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
(71−61, 71, 244)-Net over F81 — Digital
Digital (10, 71, 244)-net over F81, using
- t-expansion [i] based on digital (9, 71, 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
(71−61, 71, 4259)-Net in Base 81 — Upper bound on s
There is no (10, 71, 4260)-net in base 81, because
- 1 times m-reduction [i] would yield (10, 70, 4260)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 39 510408 394447 084147 048432 657162 918916 388461 626533 579234 750840 160732 296855 880936 680147 243810 826735 162067 818821 293073 737408 709831 344001 > 8170 [i]