MinT - Best Known (87−52, 87, s)-Nets in Base 4

Best Known (87−52, 87, s)-Nets in Base 4

(87−52, 87, 56)-Net over F₄ — Constructive and digital

Digital (35, 87, 56)-net over F₄, using

t-expansion [i] based on digital (33, 87, 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]

(87−52, 87, 65)-Net over F₄ — Digital

Digital (35, 87, 65)-net over F₄, using

t-expansion [i] based on digital (33, 87, 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]

(87−52, 87, 343)-Net in Base 4 — Upper bound on s

There is no (35, 87, 344)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 25709 140620 027404 831709 398965 539031 004674 966627 684984 > 4⁸⁷ [i]