MinT - Best Known (43−31, 43, s)-Nets in Base 4

Best Known (43−31, 43, s)-Nets in Base 4

(43−31, 43, 28)-Net over F₄ — Constructive and digital

Digital (12, 43, 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]

(43−31, 43, 29)-Net over F₄ — Digital

Digital (12, 43, 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]

(43−31, 43, 83)-Net in Base 4 — Upper bound on s

There is no (12, 43, 84)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁴³, 84, S₄, 31), but
- the linear programming bound shows that MÂ â‰¥ 743 432824 923585 138466 079893 608385 692163 936496 473876 252564 706270 846821 427655 153621 009913 103585 162421 132960 451704 728431 099904 / 9 052373 288486 345160 206941 767894 606217 335850 613093 145925 916389 354432 331859 732314 014078 839167 611385 > 4⁴³ [i]