MinT - Best Known (56, 104, s)-Nets in Base 4

Best Known (56, 104, s)-Nets in Base 4

(56, 104, 90)-Net over F₄ — Constructive and digital

Digital (56, 104, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 52, 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]

(56, 104, 107)-Net over F₄ — Digital

Digital (56, 104, 107)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 104, 1308)-Net in Base 4 — Upper bound on s

There is no (56, 104, 1309)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 414 975443 416056 481525 828873 766418 359803 849819 614835 066692 405451 > 4¹⁰⁴ [i]