Best Known (186−71, 186, s)-Nets in Base 3
(186−71, 186, 156)-Net over F3 — Constructive and digital
Digital (115, 186, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 93, 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
(186−71, 186, 201)-Net over F3 — Digital
Digital (115, 186, 201)-net over F3, using
(186−71, 186, 2278)-Net in Base 3 — Upper bound on s
There is no (115, 186, 2279)-net in base 3, because
- 1 times m-reduction [i] would yield (115, 185, 2279)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 18614 413046 658217 027696 882133 075192 655209 697988 829111 581290 359647 872131 141390 900444 190555 > 3185 [i]