MinT - Best Known (44−32, 44, s)-Nets in Base 4

Best Known (44−32, 44, s)-Nets in Base 4

(44−32, 44, 28)-Net over F₄ — Constructive and digital

Digital (12, 44, 28)-net over F₄, using

net from sequence [i] based on digital (12, 27)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 28, using
  - an explicitly constructive algebraic function field [i]

(44−32, 44, 29)-Net over F₄ — Digital

Digital (12, 44, 29)-net over F₄, using

net from sequence [i] based on digital (12, 28)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 29, using
  - a curve from the manYPoints database [i]

(44−32, 44, 77)-Net in Base 4 — Upper bound on s

There is no (12, 44, 78)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁴⁴, 78, S₄, 32), but
- the linear programming bound shows that MÂ â‰¥ 6494 701973 319596 319411 505644 198758 912380 987156 559373 341853 371003 305984 / 20 900504 425646 782891 884802 386525 565227 186175 > 4⁴⁴ [i]