MinT - Best Known (58, 58+50, s)-Nets in Base 4

Best Known (58, 58+50, s)-Nets in Base 4

(58, 58+50, 90)-Net over F₄ — Constructive and digital

Digital (58, 108, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 54, 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]

(58, 58+50, 109)-Net over F₄ — Digital

Digital (58, 108, 109)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+50, 1333)-Net in Base 4 — Upper bound on s

There is no (58, 108, 1334)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 107050 562901 309070 997164 671263 301023 182221 788966 404583 119100 130988 > 4¹⁰⁸ [i]