MinT - Best Known (98−60, 98, s)-Nets in Base 3

Best Known (98−60, 98, s)-Nets in Base 3

(98−60, 98, 38)-Net over F₃ — Constructive and digital

Digital (38, 98, 38)-net over F₃, using

t-expansion [i] based on digital (32, 98, 38)-net over F₃, using
- net from sequence [i] based on digital (32, 37)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 32 and N(F) ≥ 38, using
    - an explicitly constructive algebraic function field [i]

(98−60, 98, 52)-Net over F₃ — Digital

Digital (38, 98, 52)-net over F₃, using

t-expansion [i] based on digital (37, 98, 52)-net over F₃, using
- net from sequence [i] based on digital (37, 51)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 37 and N(F) ≥ 52, using
    - a curve from the manYPoints database [i]

(98−60, 98, 148)-Net in Base 3 — Upper bound on s

There is no (38, 98, 149)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁹⁸, 149, S₃, 60), but
- the linear programming bound shows that MÂ â‰¥ 175 563963 876147 866819 088546 989967 431479 939179 997745 088660 249738 269689 670196 162873 / 2919 602909 859501 396896 313455 231725 > 3⁹⁸ [i]