MinT - Best Known (187−73, 187, s)-Nets in Base 3

Best Known (187−73, 187, s)-Nets in Base 3

(187−73, 187, 148)-Net over F₃ — Constructive and digital

Digital (114, 187, 148)-net over F₃, using

7 times m-reduction [i] based on digital (114, 194, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 97, 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]

(187−73, 187, 189)-Net over F₃ — Digital

Digital (114, 187, 189)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(187−73, 187, 2048)-Net in Base 3 — Upper bound on s

There is no (114, 187, 2049)-net in base 3, because

1 times m-reduction [i] would yield (114, 186, 2049)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 56070 784411 080667 906845 038049 299916 632250 379147 239450 198510 269435 057510 577670 552867 964625 > 3¹⁸⁶ [i]