Best Known (115, 115+82, s)-Nets in Base 4
(115, 115+82, 130)-Net over F4 — Constructive and digital
Digital (115, 197, 130)-net over F4, using
- t-expansion [i] based on digital (105, 197, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(115, 115+82, 254)-Net over F4 — Digital
Digital (115, 197, 254)-net over F4, using
(115, 115+82, 4169)-Net in Base 4 — Upper bound on s
There is no (115, 197, 4170)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 40352 060965 093610 082783 140106 174348 281278 762850 255362 863131 810323 721851 446403 048072 702117 138604 174142 059735 928324 090754 > 4197 [i]