MinT - Best Known (188−75, 188, s)-Nets in Base 3

Best Known (188−75, 188, s)-Nets in Base 3

(188−75, 188, 148)-Net over F₃ — Constructive and digital

Digital (113, 188, 148)-net over F₃, using

4 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]

(188−75, 188, 178)-Net over F₃ — Digital

Digital (113, 188, 178)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(188−75, 188, 1852)-Net in Base 3 — Upper bound on s

There is no (113, 188, 1853)-net in base 3, because

1 times m-reduction [i] would yield (113, 187, 1853)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 166621 137978 068917 252400 079727 256921 880188 086461 944762 854884 089984 193921 863090 112510 213643 > 3¹⁸⁷ [i]