MinT - Best Known (55−35, 55, s)-Nets in Base 3

Best Known (55−35, 55, s)-Nets in Base 3

(55−35, 55, 28)-Net over F₃ — Constructive and digital

Digital (20, 55, 28)-net over F₃, using

t-expansion [i] based on digital (15, 55, 28)-net over F₃, using
- net from sequence [i] based on digital (15, 27)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]

(55−35, 55, 32)-Net over F₃ — Digital

Digital (20, 55, 32)-net over F₃, using

t-expansion [i] based on digital (19, 55, 32)-net over F₃, using
- net from sequence [i] based on digital (19, 31)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 19 and N(F) ≥ 32, using
    - a curve from the manYPoints database [i]

(55−35, 55, 86)-Net in Base 3 — Upper bound on s

There is no (20, 55, 87)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁵⁵, 87, S₃, 35), but
- the linear programming bound shows that MÂ â‰¥ 4 080243 847169 139626 292321 742040 788787 487274 687791 / 20316 463038 499354 974208 > 3⁵⁵ [i]