Best Known (10, s)-Sequences in Base 5
(10, 25)-Sequence over F5 — Constructive and digital
Digital (10, 25)-sequence over F5, using
- t-expansion [i] based on digital (9, 25)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 9 and N(F) ≥ 26, using
(10, 26)-Sequence over F5 — Digital
Digital (10, 26)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 10 and N(F) ≥ 27, using
(10, 52)-Sequence in Base 5 — Upper bound on s
There is no (10, 53)-sequence in base 5, because
- net from sequence [i] would yield (10, m, 54)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (10, 105, 54)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5105, 54, S5, 2, 95), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 123 259516 440783 094595 582588 325435 348386 438505 485784 844495 356082 916259 765625 / 4 > 5105 [i]
- extracting embedded OOA [i] would yield OOA(5105, 54, S5, 2, 95), but
- m-reduction [i] would yield (10, 105, 54)-net in base 5, but