Best Known (79, 79+140, s)-Nets in Base 4
(79, 79+140, 104)-Net over F4 — Constructive and digital
Digital (79, 219, 104)-net over F4, using
- t-expansion [i] based on digital (73, 219, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the 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) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
(79, 79+140, 112)-Net over F4 — Digital
Digital (79, 219, 112)-net over F4, using
- t-expansion [i] based on digital (73, 219, 112)-net over F4, using
- net from sequence [i] based on digital (73, 111)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 112, using
- net from sequence [i] based on digital (73, 111)-sequence over F4, using
(79, 79+140, 629)-Net in Base 4 — Upper bound on s
There is no (79, 219, 630)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 732877 662697 427301 784012 246688 029499 149623 002487 335247 319356 931397 870173 636691 195985 650853 286302 169351 680276 043143 585702 167548 348096 > 4219 [i]