MinT - Best Known (92−33, 92, s)-Nets in Base 4

Best Known (92−33, 92, s)-Nets in Base 4

(92−33, 92, 130)-Net over F₄ — Constructive and digital

Digital (59, 92, 130)-net over F₄, using

14 times m-reduction [i] based on digital (59, 106, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 53, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(92−33, 92, 223)-Net over F₄ — Digital

Digital (59, 92, 223)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(92−33, 92, 6007)-Net in Base 4 — Upper bound on s

There is no (59, 92, 6008)-net in base 4, because

1 times m-reduction [i] would yield (59, 91, 6008)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6 134990 874101 187923 579948 843495 176826 754228 256487 536375 > 4⁹¹ [i]