Best Known (125, 125+100, s)-Nets in Base 4
(125, 125+100, 130)-Net over F4 — Constructive and digital
Digital (125, 225, 130)-net over F4, using
- t-expansion [i] based on digital (105, 225, 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
(125, 125+100, 231)-Net over F4 — Digital
Digital (125, 225, 231)-net over F4, using
(125, 125+100, 3284)-Net in Base 4 — Upper bound on s
There is no (125, 225, 3285)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2943 903593 806597 386343 540761 235599 721338 241639 936916 437949 622731 014926 211104 014772 534111 893147 083272 077744 806306 858340 965814 180578 004500 > 4225 [i]