Best Known (144−74, 144, s)-Nets in Base 9
(144−74, 144, 165)-Net over F9 — Constructive and digital
Digital (70, 144, 165)-net over F9, using
- t-expansion [i] based on digital (64, 144, 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
(144−74, 144, 238)-Net over F9 — Digital
Digital (70, 144, 238)-net over F9, using
(144−74, 144, 9453)-Net in Base 9 — Upper bound on s
There is no (70, 144, 9454)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 258078 869212 225742 945083 059646 940973 302421 383029 153173 203270 968307 827468 018546 282539 218608 540393 201233 988414 242094 382085 119410 313311 942065 > 9144 [i]