Best Known (14, s)-Sequences in Base 5
(14, 34)-Sequence over F5 — Constructive and digital
Digital (14, 34)-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 3 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]
(14, 38)-Sequence over F5 — Digital
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
(14, 68)-Sequence in Base 5 — Upper bound on s
There is no (14, 69)-sequence in base 5, because
- net from sequence [i] would yield (14, m, 70)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (14, 206, 70)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5206, 70, S5, 3, 192), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 218 777880 862305 763141 783501 890707 492833 251052 806603 532023 086130 988700 349634 056449 104123 060188 013369 346143 356664 047274 762197 048403 322696 685791 015625 / 193 > 5206 [i]
- extracting embedded OOA [i] would yield OOA(5206, 70, S5, 3, 192), but
- m-reduction [i] would yield (14, 206, 70)-net in base 5, but