Best Known (41−32, 41, s)-Nets in Base 81
(41−32, 41, 172)-Net over F81 — Constructive and digital
Digital (9, 41, 172)-net over F81, using
- t-expansion [i] based on digital (7, 41, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
(41−32, 41, 244)-Net over F81 — Digital
Digital (9, 41, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
(41−32, 41, 6598)-Net in Base 81 — Upper bound on s
There is no (9, 41, 6599)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 1 772440 442270 316925 974735 899975 795928 856651 304089 058917 851823 957701 444130 046721 > 8141 [i]