Best Known (3, s)-Sequences in Base 5
(3, 15)-Sequence over F5 — Constructive and digital
Digital (3, 15)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 3 and N(F) ≥ 16, using
(3, 19)-Sequence in Base 5 — Upper bound on s
There is no (3, 20)-sequence in base 5, because
- net from sequence [i] would yield (3, m, 21)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (3, 23, 21)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(523, 21, S5, 2, 20), but
- the linear programming bound for OOAs shows that M ≥ 12 767314 910888 671875 / 1049 > 523 [i]
- extracting embedded OOA [i] would yield OOA(523, 21, S5, 2, 20), but
- m-reduction [i] would yield (3, 23, 21)-net in base 5, but