Best Known (25, 25+66, s)-Nets in Base 9
(25, 25+66, 78)-Net over F9 — Constructive and digital
Digital (25, 91, 78)-net over F9, using
- t-expansion [i] based on digital (22, 91, 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+66, 96)-Net over F9 — Digital
Digital (25, 91, 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+66, 684)-Net in Base 9 — Upper bound on s
There is no (25, 91, 685)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 712 288086 102420 577671 891328 333405 839911 017828 837181 179035 636083 810037 739539 556784 524905 > 991 [i]