MinT - Best Known (60−38, 60, s)-Nets in Base 4

Best Known (60−38, 60, s)-Nets in Base 4

(60−38, 60, 34)-Net over F₄ — Constructive and digital

Digital (22, 60, 34)-net over F₄, using

t-expansion [i] based on digital (21, 60, 34)-net over F₄, using
- net from sequence [i] based on digital (21, 33)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
    - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(60−38, 60, 44)-Net over F₄ — Digital

Digital (22, 60, 44)-net over F₄, using

t-expansion [i] based on digital (21, 60, 44)-net over F₄, using
- net from sequence [i] based on digital (21, 43)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 44, using
    - a curve from the manYPoints database [i]

(60−38, 60, 195)-Net in Base 4 — Upper bound on s

There is no (22, 60, 196)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 375088 459588 283980 788094 523528 702796 > 4⁶⁰ [i]