Best Known (52, 52+80, s)-Nets in Base 9
(52, 52+80, 81)-Net over F9 — Constructive and digital
Digital (52, 132, 81)-net over F9, using
- t-expansion [i] based on digital (32, 132, 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
(52, 52+80, 84)-Net in Base 9 — Constructive
(52, 132, 84)-net in base 9, using
- base change [i] based on digital (8, 88, 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
(52, 52+80, 182)-Net over F9 — Digital
Digital (52, 132, 182)-net over F9, using
- t-expansion [i] based on digital (50, 132, 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
(52, 52+80, 2753)-Net in Base 9 — Upper bound on s
There is no (52, 132, 2754)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 920396 795577 408156 464518 920727 883700 171053 782356 174779 278328 440834 116353 062483 289773 335786 753428 476641 518524 041945 207423 269761 > 9132 [i]