MinT - Best Known (55−40, 55, s)-Nets in Base 4

Best Known (55−40, 55, s)-Nets in Base 4

(55−40, 55, 33)-Net over F₄ — Constructive and digital

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]

(55−40, 55, 35)-Net over F₄ — Digital

Digital (15, 55, 35)-net over F₄, using

net from sequence [i] based on digital (15, 34)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 35, using
  - a curve from the manYPoints database [i]

(55−40, 55, 81)-Net in Base 4 — Upper bound on s

There is no (15, 55, 82)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁵⁵, 82, S₄, 40), but
- the linear programming bound shows that MÂ â‰¥ 107905 021301 419780 483625 545678 890111 036273 077132 460032 / 75 305424 318160 354325 > 4⁵⁵ [i]