Best Known (7, s)-Sequences in Base 5
(7, 21)-Sequence over F5 — Constructive and digital
Digital (7, 21)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 7 and N(F) ≥ 22, using
(7, 38)-Sequence in Base 5 — Upper bound on s
There is no (7, 39)-sequence in base 5, because
- net from sequence [i] would yield (7, m, 40)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (7, 77, 40)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(577, 40, S5, 2, 70), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 49 630836 753181 660492 284521 524197 771213 948726 654052 734375 / 71 > 577 [i]
- extracting embedded OOA [i] would yield OOA(577, 40, S5, 2, 70), but
- m-reduction [i] would yield (7, 77, 40)-net in base 5, but