MinT - Best Known (18, 55, s)-Nets in Base 4

Best Known (18, 55, s)-Nets in Base 4

(18, 55, 33)-Net over F₄ — Constructive and digital

Digital (18, 55, 33)-net over F₄, using

t-expansion [i] based on digital (15, 55, 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]

(18, 55, 41)-Net over F₄ — Digital

Digital (18, 55, 41)-net over F₄, using

net from sequence [i] based on digital (18, 40)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 18 and N(F) ≥ 41, using
  - Drinfeld modules of rank 1 [i]

(18, 55, 143)-Net in Base 4 — Upper bound on s

There is no (18, 55, 144)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁵⁵, 144, S₄, 37), but
- the linear programming bound shows that MÂ â‰¥ 8531 459492 474233 301926 174796 532559 659169 361619 057384 079100 594036 798926 268886 155264 000000 / 6 295882 403116 171983 140577 568447 723788 871703 289647 780291 > 4⁵⁵ [i]