MinT - Best Known (14, s)-Sequences in Base 4

Best Known (14, s)-Sequences in Base 4

(14, 29)-Sequence over F₄ — Constructive and digital

Digital (14, 29)-sequence over F₄, using

t-expansion [i] based on digital (13, 29)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
  - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(14, 32)-Sequence over F₄ — Digital

Digital (14, 32)-sequence over F₄, using

t-expansion [i] based on digital (13, 32)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 33, using
  - Drinfeld modules of rank 1 [i]

(14, 52)-Sequence in Base 4 — Upper bound on s

There is no (14, 53)-sequence in base 4, because

net from sequence [i] would yield (14, m, 54)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (14, 158, 54)-net in base 4, but
  - extracting embedded OOA [i] would yield OOA(4¹⁵⁸, 54, S₄, 3, 144), but
    - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 24 563850 913090 465947 542749 620949 849317 931102 007101 506854 390978 489955 526846 477366 325264 063999 770624 / 145 > 4¹⁵⁸ [i]