MinT - Best Known (112−32, 112, s)-Nets in Base 4

Best Known (112−32, 112, s)-Nets in Base 4

(112−32, 112, 384)-Net over F₄ — Constructive and digital

Digital (80, 112, 384)-net over F₄, using

4¹ times duplication [i] based on digital (79, 111, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 37, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(112−32, 112, 635)-Net over F₄ — Digital

Digital (80, 112, 635)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(112−32, 112, 37126)-Net in Base 4 — Upper bound on s

There is no (80, 112, 37127)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 26 962450 914309 871024 064188 839401 208148 882455 429017 508446 852992 259248 > 4¹¹² [i]