MinT - Best Known (36, 36+67, s)-Nets in Base 3

Best Known (36, 36+67, s)-Nets in Base 3

(36, 36+67, 38)-Net over F₃ — Constructive and digital

Digital (36, 103, 38)-net over F₃, using

t-expansion [i] based on digital (32, 103, 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+67, 48)-Net over F₃ — Digital

Digital (36, 103, 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+67, 118)-Net in Base 3 — Upper bound on s

There is no (36, 103, 119)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹⁰³, 119, S₃, 67), but
- the linear programming bound shows that MÂ â‰¥ 821678 234986 022501 332043 817791 314604 358242 170799 200323 / 45353 > 3¹⁰³ [i]