MinT - Best Known (133−59, 133, s)-Nets in Base 4

Best Known (133−59, 133, s)-Nets in Base 4

(133−59, 133, 130)-Net over F₄ — Constructive and digital

Digital (74, 133, 130)-net over F₄, using

3 times m-reduction [i] based on digital (74, 136, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 68, 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]

(133−59, 133, 148)-Net over F₄ — Digital

Digital (74, 133, 148)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−59, 133, 2116)-Net in Base 4 — Upper bound on s

There is no (74, 133, 2117)-net in base 4, because

1 times m-reduction [i] would yield (74, 132, 2117)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 29 875224 709775 451559 696274 928738 698094 753370 512384 332405 158446 774592 720157 614624 > 4¹³² [i]