MinT - Best Known (113−33, 113, s)-Nets in Base 4

Best Known (113−33, 113, s)-Nets in Base 4

(113−33, 113, 312)-Net over F₄ — Constructive and digital

Digital (80, 113, 312)-net over F₄, using

t-expansion [i] based on digital (79, 113, 312)-net over F₄, using
- 1 times m-reduction [i] based on digital (79, 114, 312)-net over F₄, using
  - trace code for nets [i] based on digital (3, 38, 104)-net over F₆₄, using
    - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]

(113−33, 113, 586)-Net over F₄ — Digital

Digital (80, 113, 586)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(113−33, 113, 37126)-Net in Base 4 — Upper bound on s

There is no (80, 113, 37127)-net in base 4, because

1 times m-reduction [i] would yield (80, 112, 37127)-net in base 4, but
- 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]