Best Known (112, 112+98, s)-Nets in Base 4
(112, 112+98, 130)-Net over F4 — Constructive and digital
Digital (112, 210, 130)-net over F4, using
- t-expansion [i] based on digital (105, 210, 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
(112, 112+98, 186)-Net over F4 — Digital
Digital (112, 210, 186)-net over F4, using
(112, 112+98, 2383)-Net in Base 4 — Upper bound on s
There is no (112, 210, 2384)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2 739215 053311 557577 223162 332488 836271 448404 492894 003223 467506 945574 854161 899880 312564 102844 691740 057577 302403 036591 789157 977284 > 4210 [i]