MinT - Best Known (117−74, 117, s)-Nets in Base 3

Best Known (117−74, 117, s)-Nets in Base 3

(117−74, 117, 42)-Net over F₃ — Constructive and digital

Digital (43, 117, 42)-net over F₃, using

t-expansion [i] based on digital (39, 117, 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]

(117−74, 117, 56)-Net over F₃ — Digital

Digital (43, 117, 56)-net over F₃, using

t-expansion [i] based on digital (40, 117, 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]

(117−74, 117, 143)-Net in Base 3 — Upper bound on s

There is no (43, 117, 144)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹¹⁷, 144, S₃, 74), but
- the linear programming bound shows that MÂ â‰¥ 4381 059426 646764 259966 116228 241176 370504 380611 796046 800862 061400 533793 / 53 538418 767925 > 3¹¹⁷ [i]