MinT - Best Known (12, 41, s)-Nets in Base 4

Best Known (12, 41, s)-Nets in Base 4

(12, 41, 28)-Net over F₄ — Constructive and digital

Digital (12, 41, 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]

(12, 41, 29)-Net over F₄ — Digital

Digital (12, 41, 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]

(12, 41, 91)-Net in Base 4 — Upper bound on s

There is no (12, 41, 92)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁴¹, 92, S₄, 29), but
- the linear programming bound shows that MÂ â‰¥ 8291 138749 676505 103841 959950 541753 992228 411787 128227 036594 724129 251790 946304 / 1649 446049 086149 969896 114658 918272 865279 146667 501047 > 4⁴¹ [i]