Best Known (13, 13+222, s)-Nets in Base 4
(13, 13+222, 30)-Net over F4 — Constructive and digital
Digital (13, 235, 30)-net over F4, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 13 and N(F) ≥ 30, using
- F4 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) = 13 and N(F) ≥ 30, using
(13, 13+222, 33)-Net over F4 — Digital
Digital (13, 235, 33)-net over F4, using
- net from sequence [i] based on digital (13, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 13 and N(F) ≥ 33, using
(13, 13+222, 50)-Net in Base 4 — Upper bound on s
There is no (13, 235, 51)-net in base 4, because
- 86 times m-reduction [i] would yield (13, 149, 51)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4149, 51, S4, 3, 136), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 95 740690 887720 846054 616947 355240 773569 419014 502299 003779 898601 119655 921088 876825 190619 676672 / 137 > 4149 [i]
- extracting embedded OOA [i] would yield OOA(4149, 51, S4, 3, 136), but