MinT - Best Known (59−43, 59, s)-Nets in Base 4

Best Known (59−43, 59, s)-Nets in Base 4

(59−43, 59, 33)-Net over F₄ — Constructive and digital

Digital (16, 59, 33)-net over F₄, using

t-expansion [i] based on digital (15, 59, 33)-net over F₄, using
- net from sequence [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]

(59−43, 59, 36)-Net over F₄ — Digital

Digital (16, 59, 36)-net over F₄, using

net from sequence [i] based on 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]

(59−43, 59, 81)-Net in Base 4 — Upper bound on s

There is no (16, 59, 82)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁵⁹, 82, S₄, 43), but
- the linear programming bound shows that MÂ â‰¥ 113 303848 813251 769790 373484 570498 790503 594690 871296 / 335 930280 888125 > 4⁵⁹ [i]