MinT - Best Known (58, 58+52, s)-Nets in Base 4

Best Known (58, 58+52, s)-Nets in Base 4

(58, 58+52, 76)-Net over F₄ — Constructive and digital

Digital (58, 110, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 55, 38)-net over F₁₆, using
- net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]

(58, 58+52, 104)-Net over F₄ — Digital

Digital (58, 110, 104)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+52, 1218)-Net in Base 4 — Upper bound on s

There is no (58, 110, 1219)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 693398 081900 581617 500056 576598 954106 488338 635196 983292 914909 055224 > 4¹¹⁰ [i]