MinT - Best Known (140−64, 140, s)-Nets in Base 4

Best Known (140−64, 140, s)-Nets in Base 4

(140−64, 140, 130)-Net over F₄ — Constructive and digital

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]

(140−64, 140, 140)-Net over F₄ — Digital

Digital (76, 140, 140)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−64, 140, 1809)-Net in Base 4 — Upper bound on s

There is no (76, 140, 1810)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 958029 408805 165968 062013 106118 415288 289640 429952 652876 099019 388429 722196 395584 402200 > 4¹⁴⁰ [i]