MinT - Best Known (120, 159, s)-Nets in Base 4

Best Known (120, 159, s)-Nets in Base 4

(120, 159, 1028)-Net over F₄ — Constructive and digital

Digital (120, 159, 1028)-net over F₄, using

1 times m-reduction [i] based on digital (120, 160, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 40, 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]

(120, 159, 1674)-Net over F₄ — Digital

Digital (120, 159, 1674)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(120, 159, 268332)-Net in Base 4 — Upper bound on s

There is no (120, 159, 268333)-net in base 4, because

1 times m-reduction [i] would yield (120, 158, 268333)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 133502 178234 966878 345491 877640 882049 911424 367412 897439 852099 408962 978839 109908 742312 352254 011608 > 4¹⁵⁸ [i]