Best Known (7, s)-Sequences in Base 4
(7, 20)-Sequence over F4 — Constructive and digital
Digital (7, 20)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 7 and N(F) ≥ 21, using
(7, 30)-Sequence in Base 4 — Upper bound on s
There is no (7, 31)-sequence in base 4, because
- net from sequence [i] would yield (7, m, 32)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (7, 61, 32)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(461, 32, S4, 2, 54), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 340 282366 920938 463463 374607 431768 211456 / 55 > 461 [i]
- extracting embedded OOA [i] would yield OOA(461, 32, S4, 2, 54), but
- m-reduction [i] would yield (7, 61, 32)-net in base 4, but