Best Known (51−47, 51, s)-Nets in Base 5
(51−47, 51, 18)-Net over F5 — Constructive and digital
Digital (4, 51, 18)-net over F5, using
- net from sequence [i] based on digital (4, 17)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 4 and N(F) ≥ 18, using
(51−47, 51, 24)-Net in Base 5 — Upper bound on s
There is no (4, 51, 25)-net in base 5, because
- 22 times m-reduction [i] would yield (4, 29, 25)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(529, 25, S5, 2, 25), but
- the linear programming bound for OOAs shows that M ≥ 120468 437671 661376 953125 / 639 > 529 [i]
- extracting embedded OOA [i] would yield OOA(529, 25, S5, 2, 25), but