MinT - Best Known (188−76, 188, s)-Nets in Base 3

Best Known (188−76, 188, s)-Nets in Base 3

(188−76, 188, 148)-Net over F₃ — Constructive and digital

Digital (112, 188, 148)-net over F₃, using

2 times m-reduction [i] based on digital (112, 190, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 95, 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]

(188−76, 188, 172)-Net over F₃ — Digital

Digital (112, 188, 172)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(188−76, 188, 1685)-Net in Base 3 — Upper bound on s

There is no (112, 188, 1686)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 502370 320289 887266 439284 810697 894708 760902 469612 928187 304082 336332 034723 215734 118097 564533 > 3¹⁸⁸ [i]