MinT - Best Known (37, s)-Sequences in Base 2

Best Known (37, s)-Sequences in Base 2

(37, 23)-Sequence over F₂ — Constructive and digital

Digital (37, 23)-sequence over F₂, using

t-expansion [i] based on digital (33, 23)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 33 and N(F) ≥ 24, using
  - a function field by SÃ©mirat [i]

(37, 29)-Sequence over F₂ — Digital

Digital (37, 29)-sequence over F₂, using

t-expansion [i] based on digital (36, 29)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 36 and N(F) ≥ 30, using
  - Drinfeld modules of rank 1 [i]

(37, 44)-Sequence in Base 2 — Upper bound on s

There is no (37, 45)-sequence in base 2, because

net from sequence [i] would yield (37, m, 46)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (37, 223, 46)-net in base 2, but
  - extracting embedded OOA [i] would yield OOA(2²²³, 46, S₂, 5, 186), but
    - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 2695 994666 715063 979466 701508 701963 067363 714442 254057 248110 361024 921600 / 187 > 2²²³ [i]