MinT - Best Known (140−54, 140, s)-Nets in Base 4

Best Known (140−54, 140, s)-Nets in Base 4

(140−54, 140, 130)-Net over F₄ — Constructive and digital

Digital (86, 140, 130)-net over F₄, using

20 times m-reduction [i] based on digital (86, 160, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 80, 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]

(140−54, 140, 244)-Net over F₄ — Digital

Digital (86, 140, 244)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−54, 140, 4798)-Net in Base 4 — Upper bound on s

There is no (86, 140, 4799)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 949395 024471 084914 709169 437015 952268 806628 093729 145255 260910 208503 865261 408458 091440 > 4¹⁴⁰ [i]