MinT - Best Known (90−56, 90, s)-Nets in Base 4

Best Known (90−56, 90, s)-Nets in Base 4

(90−56, 90, 56)-Net over F₄ — Constructive and digital

Digital (34, 90, 56)-net over F₄, using

t-expansion [i] based on digital (33, 90, 56)-net over F₄, using
- net from sequence [i] based on digital (33, 55)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(90−56, 90, 65)-Net over F₄ — Digital

Digital (34, 90, 65)-net over F₄, using

t-expansion [i] based on digital (33, 90, 65)-net over F₄, using
- net from sequence [i] based on digital (33, 64)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 65, using
    - Drinfeld modules of rank 1 [i]

(90−56, 90, 299)-Net in Base 4 — Upper bound on s

There is no (34, 90, 300)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁹⁰, 300, S₄, 56), but
- the linear programming bound shows that MÂ â‰¥ 436432 663383 056419 717825 118031 037669 695806 931459 228146 549597 109866 228835 207497 684949 420603 397716 437702 445220 085958 062968 094084 353631 453184 / 252220 182913 707539 004210 070528 097549 966949 311513 543692 315598 955307 835461 085957 375101 > 4⁹⁰ [i]