MinT - Best Known (60, 60+52, s)-Nets in Base 4

Best Known (60, 60+52, s)-Nets in Base 4

(60, 60+52, 90)-Net over F₄ — Constructive and digital

Digital (60, 112, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 56, 45)-net over F₁₆, using
- net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
    - a function field by GarcÃa and Quoos [i]

(60, 60+52, 111)-Net over F₄ — Digital

Digital (60, 112, 111)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+52, 1358)-Net in Base 4 — Upper bound on s

There is no (60, 112, 1359)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 27 336225 394500 544960 021013 435773 880653 992463 288490 757314 340661 557988 > 4¹¹² [i]