MinT - Best Known (44, 44+46, s)-Nets in Base 4

Best Known (44, 44+46, s)-Nets in Base 4

(44, 44+46, 56)-Net over F₄ — Constructive and digital

Digital (44, 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]

(44, 44+46, 65)-Net in Base 4 — Constructive

(44, 90, 65)-net in base 4, using

base change [i] based on digital (14, 60, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(44, 44+46, 75)-Net over F₄ — Digital

Digital (44, 90, 75)-net over F₄, using

t-expansion [i] based on digital (40, 90, 75)-net over F₄, using
- net from sequence [i] based on digital (40, 74)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 40 and N(F) ≥ 75, using
    - Drinfeld modules of rank 1 [i]

(44, 44+46, 694)-Net in Base 4 — Upper bound on s

There is no (44, 90, 695)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 545561 873635 247607 292586 018794 306638 315844 759333 422084 > 4⁹⁰ [i]