Best Known (25, 25+108, s)-Nets in Base 9
(25, 25+108, 78)-Net over F9 — Constructive and digital
Digital (25, 133, 78)-net over F9, using
- t-expansion [i] based on digital (22, 133, 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+108, 96)-Net over F9 — Digital
Digital (25, 133, 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+108, 554)-Net in Base 9 — Upper bound on s
There is no (25, 133, 555)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 8 678915 366876 262642 399253 938266 439947 471159 165588 828367 669026 423154 724084 284110 763381 988339 236541 775822 827053 962870 584613 636113 > 9133 [i]