Best Known (31, 31+50, s)-Nets in Base 9
(31, 31+50, 78)-Net over F9 — Constructive and digital
Digital (31, 81, 78)-net over F9, using
- t-expansion [i] based on digital (22, 81, 78)-net over F9, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
(31, 31+50, 120)-Net over F9 — Digital
Digital (31, 81, 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
(31, 31+50, 1556)-Net in Base 9 — Upper bound on s
There is no (31, 81, 1557)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 198830 228718 109918 439655 132862 521135 713262 100633 069231 985553 322572 199857 050985 > 981 [i]