MinT - Best Known (56, 56+66, s)-Nets in Base 4

Best Known (56, 56+66, s)-Nets in Base 4

(56, 56+66, 66)-Net over F₄ — Constructive and digital

Digital (56, 122, 66)-net over F₄, using

t-expansion [i] based on digital (49, 122, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(56, 56+66, 91)-Net over F₄ — Digital

Digital (56, 122, 91)-net over F₄, using

t-expansion [i] based on digital (50, 122, 91)-net over F₄, using
- net from sequence [i] based on digital (50, 90)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
    - a curve from the manYPoints database [i]

(56, 56+66, 711)-Net in Base 4 — Upper bound on s

There is no (56, 122, 712)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 29 131818 667185 340730 470021 066619 230693 309019 171711 906331 169374 261667 128370 > 4¹²² [i]