MinT - Best Known (143−35, 143, s)-Nets in Base 4

Best Known (143−35, 143, s)-Nets in Base 4

(143−35, 143, 1028)-Net over F₄ — Constructive and digital

Digital (108, 143, 1028)-net over F₄, using

1 times m-reduction [i] based on digital (108, 144, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 36, 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]

(143−35, 143, 1553)-Net over F₄ — Digital

Digital (108, 143, 1553)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−35, 143, 255724)-Net in Base 4 — Upper bound on s

There is no (108, 143, 255725)-net in base 4, because

1 times m-reduction [i] would yield (108, 142, 255725)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 31 083616 980264 478076 958303 331676 595088 096352 356678 139272 922245 178494 278971 320830 234256 > 4¹⁴² [i]