Best Known (15, s)-Sequences in Base 5
(15, 35)-Sequence over F5 — Constructive and digital
Digital (15, 35)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 11, N(F) = 32, and 4 places with degree 2 [i] based on function field F/F5 with g(F) = 11 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(15, 38)-Sequence over F5 — Digital
Digital (15, 38)-sequence over F5, using
- t-expansion [i] based on digital (14, 38)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 14 and N(F) ≥ 39, using
(15, 72)-Sequence in Base 5 — Upper bound on s
There is no (15, 73)-sequence in base 5, because
- net from sequence [i] would yield (15, m, 74)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (15, 218, 74)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5218, 74, S5, 3, 203), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 13056 405650 419723 277775 708120 647691 087053 828021 227424 328634 697487 389886 317136 615343 670538 531185 693700 127912 995358 724079 775214 477194 822393 357753 753662 109375 / 51 > 5218 [i]
- extracting embedded OOA [i] would yield OOA(5218, 74, S5, 3, 203), but
- m-reduction [i] would yield (15, 218, 74)-net in base 5, but