MinT - Best Known (238−59, 238, s)-Nets in Base 4

Best Known (238−59, 238, s)-Nets in Base 4

(238−59, 238, 1028)-Net over F₄ — Constructive and digital

Digital (179, 238, 1028)-net over F₄, using

4² times duplication [i] based on digital (177, 236, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 59, 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]

(238−59, 238, 2240)-Net over F₄ — Digital

Digital (179, 238, 2240)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−59, 238, 323781)-Net in Base 4 — Upper bound on s

There is no (179, 238, 323782)-net in base 4, because

1 times m-reduction [i] would yield (179, 237, 323782)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 48778 275008 876005 660260 944152 943846 979376 467369 223167 839500 193263 009867 697014 987417 944223 888268 825860 699835 706924 998465 418227 339981 212742 844088 > 4²³⁷ [i]