MinT - Best Known (36, 36+66, s)-Nets in Base 3

Best Known (36, 36+66, s)-Nets in Base 3

(36, 36+66, 38)-Net over F₃ — Constructive and digital

Digital (36, 102, 38)-net over F₃, using

t-expansion [i] based on digital (32, 102, 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+66, 48)-Net over F₃ — Digital

Digital (36, 102, 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+66, 120)-Net in Base 3 — Upper bound on s

There is no (36, 102, 121)-net in base 3, because

1 times m-reduction [i] would yield (36, 101, 121)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3¹⁰¹, 121, S₃, 65), but
  - the linear programming bound shows that MÂ â‰¥ 11 189025 841846 701468 756102 852145 926032 186927 338166 888349 / 5 130494 > 3¹⁰¹ [i]