MinT - Best Known (106−66, 106, s)-Nets in Base 3

Best Known (106−66, 106, s)-Nets in Base 3

(106−66, 106, 42)-Net over F₃ — Constructive and digital

Digital (40, 106, 42)-net over F₃, using

t-expansion [i] based on digital (39, 106, 42)-net over F₃, using
- net from sequence [i] based on digital (39, 41)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 39 and N(F) ≥ 42, using
    - an explicitly constructive algebraic function field [i]

(106−66, 106, 56)-Net over F₃ — Digital

Digital (40, 106, 56)-net over F₃, using

net from sequence [i] based on digital (40, 55)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 40 and N(F) ≥ 56, using
  - a curve from the manYPoints database [i]

(106−66, 106, 142)-Net in Base 3 — Upper bound on s

There is no (40, 106, 143)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹⁰⁶, 143, S₃, 66), but
- the linear programming bound shows that MÂ â‰¥ 50584 630946 042848 451389 778465 029449 231952 748470 489372 922254 899547 818597 / 106 273880 037977 292025 > 3¹⁰⁶ [i]