MinT - Best Known (34, 34+57, s)-Nets in Base 3

Best Known (34, 34+57, s)-Nets in Base 3

(34, 34+57, 38)-Net over F₃ — Constructive and digital

Digital (34, 91, 38)-net over F₃, using

t-expansion [i] based on digital (32, 91, 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+57, 46)-Net over F₃ — Digital

Digital (34, 91, 46)-net over F₃, using

t-expansion [i] based on digital (33, 91, 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+57, 125)-Net in Base 3 — Upper bound on s

There is no (34, 91, 126)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁹¹, 126, S₃, 57), but
- the linear programming bound shows that MÂ â‰¥ 522 758268 392523 485198 750869 088416 211662 177695 243345 380770 981629 125043 / 17 624856 622787 184206 086651 > 3⁹¹ [i]