MinT - Best Known (140, 140+46, s)-Nets in Base 4

Best Known (140, 140+46, s)-Nets in Base 4

(140, 140+46, 1028)-Net over F₄ — Constructive and digital

Digital (140, 186, 1028)-net over F₄, using

4² times duplication [i] based on digital (138, 184, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 46, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(140, 140+46, 1832)-Net over F₄ — Digital

Digital (140, 186, 1832)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(140, 140+46, 232344)-Net in Base 4 — Upper bound on s

There is no (140, 186, 232345)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9619 743394 371738 327168 591891 761885 872141 912564 946824 220775 118013 941344 882055 236518 269019 622721 657006 514857 082104 > 4¹⁸⁶ [i]