MinT - Best Known (140−52, 140, s)-Nets in Base 4

Best Known (140−52, 140, s)-Nets in Base 4

(140−52, 140, 130)-Net over F₄ — Constructive and digital

Digital (88, 140, 130)-net over F₄, using

24 times m-reduction [i] based on digital (88, 164, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 82, 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]

(140−52, 140, 277)-Net over F₄ — Digital

Digital (88, 140, 277)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−52, 140, 6116)-Net in Base 4 — Upper bound on s

There is no (88, 140, 6117)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 943066 026930 359113 214544 491791 919212 055967 014334 353052 404240 958932 831986 487088 991992 > 4¹⁴⁰ [i]