Best Known (145, 247, s)-Nets in Base 4
(145, 247, 138)-Net over F4 — Constructive and digital
Digital (145, 247, 138)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (21, 72, 34)-net over F4, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- T5 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) = 21 and N(F) ≥ 34, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- digital (73, 175, 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
- digital (21, 72, 34)-net over F4, using
(145, 247, 318)-Net over F4 — Digital
Digital (145, 247, 318)-net over F4, using
(145, 247, 5410)-Net in Base 4 — Upper bound on s
There is no (145, 247, 5411)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 51339 142222 305538 760760 146811 953449 587940 966211 545759 667183 093054 775829 352940 148869 289660 583794 583027 157306 299582 845465 965695 822728 174340 462258 687680 > 4247 [i]