MinT - Best Known (134−58, 134, s)-Nets in Base 4

Best Known (134−58, 134, s)-Nets in Base 4

(134−58, 134, 130)-Net over F₄ — Constructive and digital

Digital (76, 134, 130)-net over F₄, using

6 times m-reduction [i] based on digital (76, 140, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 70, 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]

(134−58, 134, 161)-Net over F₄ — Digital

Digital (76, 134, 161)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−58, 134, 2331)-Net in Base 4 — Upper bound on s

There is no (76, 134, 2332)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 479 504188 008290 601197 096670 844227 375714 277257 628462 658170 649741 830612 244349 588832 > 4¹³⁴ [i]