MinT - Best Known (36, 36+56, s)-Nets in Base 3

Best Known (36, 36+56, s)-Nets in Base 3

(36, 36+56, 38)-Net over F₃ — Constructive and digital

Digital (36, 92, 38)-net over F₃, using

t-expansion [i] based on digital (32, 92, 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]

(36, 36+56, 48)-Net over F₃ — Digital

Digital (36, 92, 48)-net over F₃, using

net from sequence [i] based on digital (36, 47)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 36 and N(F) ≥ 48, using
  - a curve from the manYPoints database [i]

(36, 36+56, 149)-Net in Base 3 — Upper bound on s

There is no (36, 92, 150)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁹², 150, S₃, 56), but
- the linear programming bound shows that MÂ â‰¥ 380 530607 134695 199590 326105 296054 561976 304500 746203 230842 591578 312022 091639 435706 399387 387663 092379 / 4 623519 949937 639772 321756 933595 131069 999192 578955 859375 > 3⁹² [i]