MinT - Best Known (36, 36+64, s)-Nets in Base 3

Best Known (36, 36+64, s)-Nets in Base 3

(36, 36+64, 38)-Net over F₃ — Constructive and digital

Digital (36, 100, 38)-net over F₃, using

t-expansion [i] based on digital (32, 100, 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+64, 48)-Net over F₃ — Digital

Digital (36, 100, 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+64, 122)-Net in Base 3 — Upper bound on s

There is no (36, 100, 123)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹⁰⁰, 123, S₃, 64), but
- the linear programming bound shows that MÂ â‰¥ 2068 950957 359319 485986 052355 872699 639826 143600 962586 698019 505123 / 2692 964647 552400 > 3¹⁰⁰ [i]