Best Known (133−66, 133, s)-Nets in Base 9
(133−66, 133, 165)-Net over F9 — Constructive and digital
Digital (67, 133, 165)-net over F9, using
- t-expansion [i] based on digital (64, 133, 165)-net over F9, using
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- T4 from the second 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) = 64 and N(F) ≥ 165, using
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
(133−66, 133, 258)-Net over F9 — Digital
Digital (67, 133, 258)-net over F9, using
(133−66, 133, 11518)-Net in Base 9 — Upper bound on s
There is no (67, 133, 11519)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 8 221972 013563 750731 909537 599442 551640 541093 782255 684126 628766 433603 188299 489717 906606 111712 406383 152365 373735 944131 606472 845049 > 9133 [i]