Best Known (108, 172, s)-Nets in Base 3
(108, 172, 156)-Net over F3 — Constructive and digital
Digital (108, 172, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 86, 78)-net over F9, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the 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) = 22 and N(F) ≥ 78, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
(108, 172, 202)-Net over F3 — Digital
Digital (108, 172, 202)-net over F3, using
(108, 172, 2314)-Net in Base 3 — Upper bound on s
There is no (108, 172, 2315)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 11620 029990 477950 460779 741217 489256 577340 192240 409674 027482 358892 874462 696641 692609 > 3172 [i]