Best Known (76, 76+125, s)-Nets in Base 4
(76, 76+125, 104)-Net over F4 — Constructive and digital
Digital (76, 201, 104)-net over F4, using
- t-expansion [i] based on digital (73, 201, 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
(76, 76+125, 112)-Net over F4 — Digital
Digital (76, 201, 112)-net over F4, using
- t-expansion [i] based on digital (73, 201, 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
(76, 76+125, 648)-Net in Base 4 — Upper bound on s
There is no (76, 201, 649)-net in base 4, because
- 1 times m-reduction [i] would yield (76, 200, 649)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2 710534 773145 698721 314334 891672 108453 682057 673448 867271 821629 878068 195901 121582 537532 553796 230437 769692 824031 719007 839040 > 4200 [i]