MinT - Best Known (134−61, 134, s)-Nets in Base 4

Best Known (134−61, 134, s)-Nets in Base 4

(134−61, 134, 130)-Net over F₄ — Constructive and digital

Digital (73, 134, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 67, 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]

(134−61, 134, 137)-Net over F₄ — Digital

Digital (73, 134, 137)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−61, 134, 1849)-Net in Base 4 — Upper bound on s

There is no (73, 134, 1850)-net in base 4, because

1 times m-reduction [i] would yield (73, 133, 1850)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 119 039457 236056 817143 695584 782897 051152 931173 853081 128267 183405 140941 738985 874928 > 4¹³³ [i]