Best Known (58, 58+92, s)-Nets in Base 9
(58, 58+92, 81)-Net over F9 — Constructive and digital
Digital (58, 150, 81)-net over F9, using
- t-expansion [i] based on digital (32, 150, 81)-net over F9, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
(58, 58+92, 84)-Net in Base 9 — Constructive
(58, 150, 84)-net in base 9, using
- base change [i] based on digital (8, 100, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
(58, 58+92, 182)-Net over F9 — Digital
Digital (58, 150, 182)-net over F9, using
- t-expansion [i] based on digital (50, 150, 182)-net over F9, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 50 and N(F) ≥ 182, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
(58, 58+92, 2881)-Net in Base 9 — Upper bound on s
There is no (58, 150, 2882)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 138616 318751 962973 005700 231045 835920 650585 920514 356359 240445 239216 361664 616798 036028 143454 149754 189560 563144 762032 541053 771814 550152 587586 518817 > 9150 [i]