MinT - Best Known (89−55, 89, s)-Nets in Base 3

Best Known (89−55, 89, s)-Nets in Base 3

(89−55, 89, 38)-Net over F₃ — Constructive and digital

Digital (34, 89, 38)-net over F₃, using

t-expansion [i] based on digital (32, 89, 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]

(89−55, 89, 46)-Net over F₃ — Digital

Digital (34, 89, 46)-net over F₃, using

t-expansion [i] based on digital (33, 89, 46)-net over F₃, using
- net from sequence [i] based on digital (33, 45)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 33 and N(F) ≥ 46, using
    - a curve from the manYPoints database [i]

(89−55, 89, 132)-Net in Base 3 — Upper bound on s

There is no (34, 89, 133)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁸⁹, 133, S₃, 55), but
- the linear programming bound shows that MÂ â‰¥ 563279 610122 744937 207502 170533 914161 505770 377850 240192 840965 900376 707282 898801 / 175286 690652 921142 892281 815302 835817 > 3⁸⁹ [i]