Best Known (29, s)-Sequences in Base 2
(29, 20)-Sequence over F2 — Constructive and digital
Digital (29, 20)-sequence over F2, using
- t-expansion [i] based on digital (21, 20)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 21 and N(F) ≥ 21, using
(29, 24)-Sequence over F2 — Digital
Digital (29, 24)-sequence over F2, using
- t-expansion [i] based on digital (28, 24)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 28 and N(F) ≥ 25, using
(29, 36)-Sequence in Base 2 — Upper bound on s
There is no (29, 37)-sequence in base 2, because
- net from sequence [i] would yield (29, m, 38)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (29, 182, 38)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2182, 38, S2, 5, 153), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 637 518145 000209 765077 072363 294528 620385 395474 828378 505216 / 77 > 2182 [i]
- extracting embedded OOA [i] would yield OOA(2182, 38, S2, 5, 153), but
- m-reduction [i] would yield (29, 182, 38)-net in base 2, but