Best Known (2, ∞, s)-Nets in Base 5
(2, ∞, 12)-Net over F5 — Constructive and digital
Digital (2, m, 12)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (2, 11)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 2 and N(F) ≥ 12, using
(2, ∞, 15)-Net in Base 5 — Upper bound on s
There is no (2, m, 16)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (2, 19, 16)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(519, 16, S5, 2, 17), but
- the linear programming bound for OOAs shows that M ≥ 3124 237060 546875 / 149 > 519 [i]
- extracting embedded OOA [i] would yield OOA(519, 16, S5, 2, 17), but