MinT - Best Known (140−58, 140, s)-Nets in Base 4

Best Known (140−58, 140, s)-Nets in Base 4

(140−58, 140, 130)-Net over F₄ — Constructive and digital

Digital (82, 140, 130)-net over F₄, using

12 times m-reduction [i] based on digital (82, 152, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 76, 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]

(140−58, 140, 192)-Net over F₄ — Digital

Digital (82, 140, 192)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−58, 140, 3113)-Net in Base 4 — Upper bound on s

There is no (82, 140, 3114)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 955691 521135 409590 028688 283112 120440 351826 309220 986516 375504 549926 179822 850004 895864 > 4¹⁴⁰ [i]