MinT - Best Known (16, s)-Sequences in Base 4

Best Known (16, s)-Sequences in Base 4

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

Digital (16, 32)-sequence over F₄, using

t-expansion [i] based on 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]

(16, 35)-Sequence over F₄ — Digital

Digital (16, 35)-sequence over F₄, using

Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 16 and N(F) ≥ 36, using
- Drinfeld modules of rank 1 [i]

(16, 58)-Sequence in Base 4 — Upper bound on s

There is no (16, 59)-sequence in base 4, because

net from sequence [i] would yield (16, m, 60)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (16, 176, 60)-net in base 4, but
  - extracting embedded OOA [i] would yield OOA(4¹⁷⁶, 60, S₄, 3, 160), but
    - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 1 614623 025657 010344 174017 910292 669206 320781 752374 469911 111262 542928 393704 766293 304881 293061 389528 483334 455296 / 161 > 4¹⁷⁶ [i]