Best Known (25, 25+112, s)-Nets in Base 9
(25, 25+112, 78)-Net over F9 — Constructive and digital
Digital (25, 137, 78)-net over F9, using
- t-expansion [i] based on digital (22, 137, 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
(25, 25+112, 96)-Net over F9 — Digital
Digital (25, 137, 96)-net over F9, using
- net from sequence [i] based on digital (25, 95)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 25 and N(F) ≥ 96, using
(25, 25+112, 552)-Net in Base 9 — Upper bound on s
There is no (25, 137, 553)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 57765 462107 177390 650898 845927 711231 181920 187033 160547 553605 398830 542780 756331 197727 097217 599589 816847 043849 432920 050533 076539 856065 > 9137 [i]