MinT - Best Known (46, 46+37, s)-Nets in Base 4

Best Known (46, 46+37, s)-Nets in Base 4

(46, 46+37, 90)-Net over F₄ — Constructive and digital

Digital (46, 83, 90)-net over F₄, using

1 times m-reduction [i] based on digital (46, 84, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 42, 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]

(46, 46+37, 100)-Net over F₄ — Digital

Digital (46, 83, 100)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(46, 46+37, 1377)-Net in Base 4 — Upper bound on s

There is no (46, 83, 1378)-net in base 4, because

1 times m-reduction [i] would yield (46, 82, 1378)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 23 433035 376398 395138 743376 608339 344363 989062 119200 > 4⁸² [i]