MinT - Best Known (131, 131+95, s)-Nets in Base 3

Best Known (131, 131+95, s)-Nets in Base 3

(131, 131+95, 148)-Net over F₃ — Constructive and digital

Digital (131, 226, 148)-net over F₃, using

2 times m-reduction [i] based on digital (131, 228, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 114, 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]

(131, 131+95, 181)-Net over F₃ — Digital

Digital (131, 226, 181)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 131+95, 1720)-Net in Base 3 — Upper bound on s

There is no (131, 226, 1721)-net in base 3, because

1 times m-reduction [i] would yield (131, 225, 1721)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 226893 431008 228887 309238 264102 702262 028170 514941 958508 358885 982250 482781 373845 732284 688087 295361 445403 995851 > 3²²⁵ [i]