MinT - Best Known (87−48, 87, s)-Nets in Base 4

Best Known (87−48, 87, s)-Nets in Base 4

(87−48, 87, 56)-Net over F₄ — Constructive and digital

Digital (39, 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]

(87−48, 87, 66)-Net over F₄ — Digital

Digital (39, 87, 66)-net over F₄, using

t-expansion [i] based on digital (37, 87, 66)-net over F₄, using
- net from sequence [i] based on digital (37, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 37 and N(F) ≥ 66, using
    - Drinfeld modules of rank 1 [i]

(87−48, 87, 478)-Net in Base 4 — Upper bound on s

There is no (39, 87, 479)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 24896 309587 701507 178482 600930 924544 387250 048844 331459 > 4⁸⁷ [i]