MinT - Best Known (11, s)-Sequences in Base 4

Best Known (11, s)-Sequences in Base 4

(11, 26)-Sequence over F₄ — Constructive and digital

Digital (11, 26)-sequence over F₄, using

t-expansion [i] based on digital (10, 26)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
  - an explicitly constructive algebraic function field [i]

(11, 43)-Sequence in Base 4 — Upper bound on s

There is no (11, 44)-sequence in base 4, because

net from sequence [i] would yield (11, m, 45)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (11, 131, 45)-net in base 4, but
  - extracting embedded OOA [i] would yield OOA(4¹³¹, 45, S₄, 3, 120), but
    - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 1452 495967 392894 355393 274435 948981 116111 418687 645795 235310 955933 795262 298203 357184 / 121 > 4¹³¹ [i]