Best Known (16, s)-Sequences in Base 5
(16, 36)-Sequence over F5 — Constructive and digital
Digital (16, 36)-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 5 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]
(16, 39)-Sequence over F5 — Digital
Digital (16, 39)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 16 and N(F) ≥ 40, using
(16, 77)-Sequence in Base 5 — Upper bound on s
There is no (16, 78)-sequence in base 5, because
- net from sequence [i] would yield (16, m, 79)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (16, 233, 79)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5233, 79, S5, 3, 217), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1340 240503 666353 430391 349655 051393 183541 014617 324592 452058 227003 710454 195151 741076 981450 654890 221798 719184 961015 937918 789070 644465 244441 789764 096029 102802 276611 328125 / 109 > 5233 [i]
- extracting embedded OOA [i] would yield OOA(5233, 79, S5, 3, 217), but
- m-reduction [i] would yield (16, 233, 79)-net in base 5, but