Best Known (129−64, 129, s)-Nets in Base 9
(129−64, 129, 165)-Net over F9 — Constructive and digital
Digital (65, 129, 165)-net over F9, using
- t-expansion [i] based on digital (64, 129, 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
(129−64, 129, 252)-Net over F9 — Digital
Digital (65, 129, 252)-net over F9, using
(129−64, 129, 11215)-Net in Base 9 — Upper bound on s
There is no (65, 129, 11216)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 1252 138600 637703 866836 278763 109604 607759 439897 172028 539066 033312 902843 965683 512875 941004 423413 573506 948249 095421 820340 809729 > 9129 [i]