Best Known (9, 9+53, s)-Nets in Base 81
(9, 9+53, 172)-Net over F81 — Constructive and digital
Digital (9, 62, 172)-net over F81, using
- t-expansion [i] based on digital (7, 62, 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
(9, 9+53, 244)-Net over F81 — Digital
Digital (9, 62, 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
(9, 9+53, 3948)-Net in Base 81 — Upper bound on s
There is no (9, 62, 3949)-net in base 81, because
- 1 times m-reduction [i] would yield (9, 61, 3949)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 263 011622 941236 027108 726869 480452 720082 158985 607084 741807 976004 718221 861762 906134 072254 422732 528598 447735 408420 213921 > 8161 [i]