MinT - Best Known (35, 35+56, s)-Nets in Base 3

Best Known (35, 35+56, s)-Nets in Base 3

(35, 35+56, 38)-Net over F₃ — Constructive and digital

Digital (35, 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]

(35, 35+56, 47)-Net over F₃ — Digital

Digital (35, 91, 47)-net over F₃, using

net from sequence [i] based on digital (35, 46)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 35 and N(F) ≥ 47, using
  - a curve from the manYPoints database [i]

(35, 35+56, 137)-Net in Base 3 — Upper bound on s

There is no (35, 91, 138)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁹¹, 138, S₃, 56), but
- the linear programming bound shows that MÂ â‰¥ 121521 787298 638889 256464 784069 369854 340084 615592 398852 377524 926497 798590 076619 / 4326 415284 402112 723012 307069 347625 > 3⁹¹ [i]