MinT - Best Known (34, 34+53, s)-Nets in Base 3

Best Known (34, 34+53, s)-Nets in Base 3

(34, 34+53, 38)-Net over F₃ — Constructive and digital

Digital (34, 87, 38)-net over F₃, using

t-expansion [i] based on digital (32, 87, 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]

(34, 34+53, 46)-Net over F₃ — Digital

Digital (34, 87, 46)-net over F₃, using

t-expansion [i] based on digital (33, 87, 46)-net over F₃, using
- net from sequence [i] based on digital (33, 45)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 33 and N(F) ≥ 46, using
    - a curve from the manYPoints database [i]

(34, 34+53, 143)-Net in Base 3 — Upper bound on s

There is no (34, 87, 144)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁸⁷, 144, S₃, 53), but
- the linear programming bound shows that MÂ â‰¥ 17223 084020 715556 855848 832250 872039 681441 493489 720994 373819 071391 134556 757302 805695 961783 787857 312694 961703 747535 992711 367021 / 52541 482507 385915 572483 476316 381490 546694 054744 799929 170031 348199 163698 205504 000000 > 3⁸⁷ [i]