Best Known (33−23, 33, s)-Nets in Base 81
(33−23, 33, 172)-Net over F81 — Constructive and digital
Digital (10, 33, 172)-net over F81, using
- t-expansion [i] based on digital (7, 33, 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
(33−23, 33, 244)-Net over F81 — Digital
Digital (10, 33, 244)-net over F81, using
- t-expansion [i] based on digital (9, 33, 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
(33−23, 33, 21866)-Net in Base 81 — Upper bound on s
There is no (10, 33, 21867)-net in base 81, because
- 1 times m-reduction [i] would yield (10, 32, 21867)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 11 793360 759760 445734 748941 698749 856986 248494 021332 831088 618961 > 8132 [i]