MinT - Best Known (35, 35+59, s)-Nets in Base 3

Best Known (35, 35+59, s)-Nets in Base 3

(35, 35+59, 38)-Net over F₃ — Constructive and digital

Digital (35, 94, 38)-net over F₃, using

t-expansion [i] based on digital (32, 94, 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+59, 47)-Net over F₃ — Digital

Digital (35, 94, 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+59, 125)-Net in Base 3 — Upper bound on s

There is no (35, 94, 126)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁹⁴, 126, S₃, 59), but
- the linear programming bound shows that MÂ â‰¥ 1676 883535 341672 540368 062818 082384 646110 411794 119026 906595 198877 / 2 350686 415945 174240 > 3⁹⁴ [i]