Best Known (1, 1+∞, s)-Nets in Base 5
(1, 1+∞, 10)-Net over F5 — Constructive and digital
Digital (1, m, 10)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (1, 9)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 1 and N(F) ≥ 10, using
(1, 1+∞, 11)-Net in Base 5 — Upper bound on s
There is no (1, m, 12)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (1, 11, 12)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(511, 12, S5, 2, 10), but
- the linear programming bound for OOAs shows that M ≥ 6103 515625 / 121 > 511 [i]
- extracting embedded OOA [i] would yield OOA(511, 12, S5, 2, 10), but