MinT - Best Known (136−51, 136, s)-Nets in Base 4

Best Known (136−51, 136, s)-Nets in Base 4

(136−51, 136, 130)-Net over F₄ — Constructive and digital

Digital (85, 136, 130)-net over F₄, using

22 times m-reduction [i] based on digital (85, 158, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 79, 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]

(136−51, 136, 262)-Net over F₄ — Digital

Digital (85, 136, 262)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−51, 136, 6027)-Net in Base 4 — Upper bound on s

There is no (85, 136, 6028)-net in base 4, because

1 times m-reduction [i] would yield (85, 135, 6028)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1897 716915 224911 919027 695466 802337 233903 490920 211304 839935 260962 634654 827772 517112 > 4¹³⁵ [i]