MinT - Best Known (214−89, 214, s)-Nets in Base 3

Best Known (214−89, 214, s)-Nets in Base 3

(214−89, 214, 148)-Net over F₃ — Constructive and digital

Digital (125, 214, 148)-net over F₃, using

2 times m-reduction [i] based on digital (125, 216, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 108, 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]

(214−89, 214, 178)-Net over F₃ — Digital

Digital (125, 214, 178)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−89, 214, 1717)-Net in Base 3 — Upper bound on s

There is no (125, 214, 1718)-net in base 3, because

1 times m-reduction [i] would yield (125, 213, 1718)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 431277 713972 495596 720697 278219 153746 875618 654049 242084 568809 049778 358644 408460 431420 718000 903018 817945 > 3²¹³ [i]