MinT - Best Known (43, 43+72, s)-Nets in Base 3

Best Known (43, 43+72, s)-Nets in Base 3

(43, 43+72, 42)-Net over F₃ — Constructive and digital

Digital (43, 115, 42)-net over F₃, using

t-expansion [i] based on digital (39, 115, 42)-net over F₃, using
- net from sequence [i] based on digital (39, 41)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 39 and N(F) ≥ 42, using
    - an explicitly constructive algebraic function field [i]

(43, 43+72, 56)-Net over F₃ — Digital

Digital (43, 115, 56)-net over F₃, using

t-expansion [i] based on digital (40, 115, 56)-net over F₃, using
- net from sequence [i] based on digital (40, 55)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 40 and N(F) ≥ 56, using
    - a curve from the manYPoints database [i]

(43, 43+72, 147)-Net in Base 3 — Upper bound on s

There is no (43, 115, 148)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹¹⁵, 148, S₃, 72), but
- the linear programming bound shows that MÂ â‰¥ 15138 532736 321222 240484 923894 686292 145850 190102 104613 028724 231594 313752 692357 / 1981 901463 555581 678825 > 3¹¹⁵ [i]