Best Known (68, 142, s)-Nets in Base 9
(68, 142, 165)-Net over F9 — Constructive and digital
Digital (68, 142, 165)-net over F9, using
- t-expansion [i] based on digital (64, 142, 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
(68, 142, 222)-Net over F9 — Digital
Digital (68, 142, 222)-net over F9, using
(68, 142, 8392)-Net in Base 9 — Upper bound on s
There is no (68, 142, 8393)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 3189 733343 758663 026431 447874 275143 914340 501956 256663 450826 860454 036230 573944 151591 934638 356929 537148 819858 319677 780379 814161 754120 302825 > 9142 [i]