MinT - Best Known (187−75, 187, s)-Nets in Base 3

Best Known (187−75, 187, s)-Nets in Base 3

(187−75, 187, 148)-Net over F₃ — Constructive and digital

Digital (112, 187, 148)-net over F₃, using

3 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]

(187−75, 187, 175)-Net over F₃ — Digital

Digital (112, 187, 175)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(187−75, 187, 1797)-Net in Base 3 — Upper bound on s

There is no (112, 187, 1798)-net in base 3, because

1 times m-reduction [i] would yield (112, 186, 1798)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 55834 216921 326375 458420 723967 892730 449052 291108 296196 887175 017118 872544 033173 204613 656485 > 3¹⁸⁶ [i]