MinT - Best Known (186−73, 186, s)-Nets in Base 3

Best Known (186−73, 186, s)-Nets in Base 3

(186−73, 186, 148)-Net over F₃ — Constructive and digital

Digital (113, 186, 148)-net over F₃, using

6 times m-reduction [i] based on digital (113, 192, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 96, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(186−73, 186, 185)-Net over F₃ — Digital

Digital (113, 186, 185)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−73, 186, 1985)-Net in Base 3 — Upper bound on s

There is no (113, 186, 1986)-net in base 3, because

1 times m-reduction [i] would yield (113, 185, 1986)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18569 699855 776571 391360 367484 979007 593276 697980 116170 921352 582131 368782 343597 506588 893801 > 3¹⁸⁵ [i]