MinT - Best Known (56, 56+50, s)-Nets in Base 4

Best Known (56, 56+50, s)-Nets in Base 4

(56, 56+50, 76)-Net over F₄ — Constructive and digital

Digital (56, 106, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 53, 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]

(56, 56+50, 101)-Net over F₄ — Digital

Digital (56, 106, 101)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+50, 1191)-Net in Base 4 — Upper bound on s

There is no (56, 106, 1192)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6710 731379 147297 780791 603480 798532 521576 631055 291596 979752 728420 > 4¹⁰⁶ [i]