MinT - Best Known (35, 35+66, s)-Nets in Base 3

Best Known (35, 35+66, s)-Nets in Base 3

(35, 35+66, 38)-Net over F₃ — Constructive and digital

Digital (35, 101, 38)-net over F₃, using

t-expansion [i] based on digital (32, 101, 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+66, 47)-Net over F₃ — Digital

Digital (35, 101, 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+66, 115)-Net in Base 3 — Upper bound on s

There is no (35, 101, 116)-net in base 3, because

1 times m-reduction [i] would yield (35, 100, 116)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3¹⁰⁰, 116, S₃, 65), but
  - the linear programming bound shows that MÂ â‰¥ 23 393290 254140 746934 441613 228589 241050 120827 369170 892591 / 37 128575 > 3¹⁰⁰ [i]