Best Known (36, s)-Sequences in Base 2
(36, 23)-Sequence over F2 — Constructive and digital
Digital (36, 23)-sequence over F2, using
- t-expansion [i] based on digital (33, 23)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 24, using
(36, 29)-Sequence over F2 — Digital
Digital (36, 29)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 36 and N(F) ≥ 30, using
(36, 43)-Sequence in Base 2 — Upper bound on s
There is no (36, 44)-sequence in base 2, because
- net from sequence [i] would yield (36, m, 45)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (36, 218, 45)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2218, 45, S2, 5, 182), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 28 644943 333847 554781 833703 529958 357590 739465 948949 358261 172585 889792 / 61 > 2218 [i]
- extracting embedded OOA [i] would yield OOA(2218, 45, S2, 5, 182), but
- m-reduction [i] would yield (36, 218, 45)-net in base 2, but