MinT - Best Known (90−56, 90, s)-Nets in Base 3

Best Known (90−56, 90, s)-Nets in Base 3

(90−56, 90, 38)-Net over F₃ — Constructive and digital

Digital (34, 90, 38)-net over F₃, using

t-expansion [i] based on digital (32, 90, 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]

(90−56, 90, 46)-Net over F₃ — Digital

Digital (34, 90, 46)-net over F₃, using

t-expansion [i] based on digital (33, 90, 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]

(90−56, 90, 128)-Net in Base 3 — Upper bound on s

There is no (34, 90, 129)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁹⁰, 129, S₃, 56), but
- the linear programming bound shows that MÂ â‰¥ 13 300088 860981 875479 508874 698822 453713 862516 001769 064578 217723 / 1 384977 750526 562500 > 3⁹⁰ [i]