Best Known (126−76, 126, s)-Nets in Base 9
(126−76, 126, 81)-Net over F9 — Constructive and digital
Digital (50, 126, 81)-net over F9, using
- t-expansion [i] based on digital (32, 126, 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
(126−76, 126, 84)-Net in Base 9 — Constructive
(50, 126, 84)-net in base 9, using
- base change [i] based on digital (8, 84, 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
(126−76, 126, 182)-Net over F9 — Digital
Digital (50, 126, 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
(126−76, 126, 2716)-Net in Base 9 — Upper bound on s
There is no (50, 126, 2717)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 1 716239 424278 109828 008836 794501 676814 338756 555701 825345 040981 223749 161145 924778 305506 225485 962406 722622 275966 639685 952945 > 9126 [i]