MinT - Best Known (156−65, 156, s)-Nets in Base 4

Best Known (156−65, 156, s)-Nets in Base 4

(156−65, 156, 130)-Net over F₄ — Constructive and digital

Digital (91, 156, 130)-net over F₄, using

14 times m-reduction [i] based on digital (91, 170, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 85, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(156−65, 156, 206)-Net over F₄ — Digital

Digital (91, 156, 206)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(156−65, 156, 3489)-Net in Base 4 — Upper bound on s

There is no (91, 156, 3490)-net in base 4, because

1 times m-reduction [i] would yield (91, 155, 3490)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2097 183011 164895 425647 697455 715107 391338 795984 287626 581011 545009 329756 182751 610461 187291 436485 > 4¹⁵⁵ [i]