MinT - Best Known (15, s)-Sequences in Base 4

Best Known (15, s)-Sequences in Base 4

(15, 32)-Sequence over F₄ — Constructive and digital

Digital (15, 32)-sequence over F₄, using

Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
- an explicitly constructive algebraic function field [i]

(15, 34)-Sequence over F₄ — Digital

Digital (15, 34)-sequence over F₄, using

Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 35, using
- a curve from the manYPoints database [i]

(15, 55)-Sequence in Base 4 — Upper bound on s

There is no (15, 56)-sequence in base 4, because

net from sequence [i] would yield (15, m, 57)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (15, 167, 57)-net in base 4, but
  - extracting embedded OOA [i] would yield OOA(4¹⁶⁷, 57, S₄, 3, 152), but
    - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 699920 231930 563815 799200 712677 638836 913014 217885 827979 656246 594051 184959 743800 295431 524216 647377 223680 / 17 > 4¹⁶⁷ [i]