MinT - Best Known (250−109, 250, s)-Nets in Base 3

Best Known (250−109, 250, s)-Nets in Base 3

(250−109, 250, 128)-Net over F₃ — Constructive and digital

Digital (141, 250, 128)-net over F₃, using

t-expansion [i] based on digital (138, 250, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 125, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(250−109, 250, 179)-Net over F₃ — Digital

Digital (141, 250, 179)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−109, 250, 1608)-Net in Base 3 — Upper bound on s

There is no (141, 250, 1609)-net in base 3, because

1 times m-reduction [i] would yield (141, 249, 1609)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 63602 127496 585064 764298 673643 971740 147357 423689 995759 171991 245044 799319 149144 028688 295822 927144 561455 126371 612577 014633 > 3²⁴⁹ [i]