Best Known (137−72, 137, s)-Nets in Base 9
(137−72, 137, 165)-Net over F9 — Constructive and digital
Digital (65, 137, 165)-net over F9, using
- t-expansion [i] based on digital (64, 137, 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
(137−72, 137, 208)-Net over F9 — Digital
Digital (65, 137, 208)-net over F9, using
(137−72, 137, 7617)-Net in Base 9 — Upper bound on s
There is no (65, 137, 7618)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 53954 435335 114860 769022 836756 707183 582288 508103 519562 822879 415612 519133 675185 784784 239023 005589 820426 088289 594509 287546 302522 675905 > 9137 [i]