Best Known (54, 138, s)-Nets in Base 9
(54, 138, 81)-Net over F9 — Constructive and digital
Digital (54, 138, 81)-net over F9, using
- t-expansion [i] based on digital (32, 138, 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
(54, 138, 84)-Net in Base 9 — Constructive
(54, 138, 84)-net in base 9, using
- base change [i] based on digital (8, 92, 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
(54, 138, 182)-Net over F9 — Digital
Digital (54, 138, 182)-net over F9, using
- t-expansion [i] based on digital (50, 138, 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
(54, 138, 2793)-Net in Base 9 — Upper bound on s
There is no (54, 138, 2794)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 490345 267866 800379 487998 551331 659977 208600 578275 966933 616087 564575 314496 248358 453717 816321 842471 881863 695672 961050 445419 881737 227745 > 9138 [i]