MinT - Best Known (195−52, 195, s)-Nets in Base 4

Best Known (195−52, 195, s)-Nets in Base 4

(195−52, 195, 531)-Net over F₄ — Constructive and digital

Digital (143, 195, 531)-net over F₄, using

9 times m-reduction [i] based on digital (143, 204, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 68, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(195−52, 195, 576)-Net in Base 4 — Constructive

(143, 195, 576)-net in base 4, using

trace code for nets [i] based on (13, 65, 192)-net in base 64, using
- 5 times m-reduction [i] based on (13, 70, 192)-net in base 64, using
  - base change [i] based on digital (3, 60, 192)-net over F₁₂₈, using
    - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(195−52, 195, 1352)-Net over F₄ — Digital

Digital (143, 195, 1352)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(195−52, 195, 115223)-Net in Base 4 — Upper bound on s

There is no (143, 195, 115224)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2521 878606 381232 432972 278063 788766 246087 690688 801438 710047 168042 384699 346508 655090 539977 172012 571008 988855 076340 517824 > 4¹⁹⁵ [i]