Best Known (72−40, 72, s)-Nets in Base 9
(72−40, 72, 81)-Net over F9 — Constructive and digital
Digital (32, 72, 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
(72−40, 72, 84)-Net in Base 9 — Constructive
(32, 72, 84)-net in base 9, using
- base change [i] based on digital (8, 48, 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
(72−40, 72, 120)-Net over F9 — Digital
Digital (32, 72, 120)-net over F9, using
- t-expansion [i] based on digital (31, 72, 120)-net over F9, using
- net from sequence [i] based on digital (31, 119)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 31 and N(F) ≥ 120, using
- net from sequence [i] based on digital (31, 119)-sequence over F9, using
(72−40, 72, 2816)-Net in Base 9 — Upper bound on s
There is no (32, 72, 2817)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 510 842601 022581 721912 022409 964578 172882 724713 128715 973217 338318 555169 > 972 [i]