Best Known (25, 25+88, s)-Nets in Base 9
(25, 25+88, 78)-Net over F9 — Constructive and digital
Digital (25, 113, 78)-net over F9, using
- t-expansion [i] based on digital (22, 113, 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+88, 96)-Net over F9 — Digital
Digital (25, 113, 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+88, 582)-Net in Base 9 — Upper bound on s
There is no (25, 113, 583)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 716275 678619 191225 415840 456294 279118 456172 308137 582900 326217 633393 946162 019816 267335 095867 916744 543309 737889 > 9113 [i]