MinT - Best Known (172−67, 172, s)-Nets in Base 3

Best Known (172−67, 172, s)-Nets in Base 3

(172−67, 172, 148)-Net over F₃ — Constructive and digital

Digital (105, 172, 148)-net over F₃, using

4 times m-reduction [i] based on digital (105, 176, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 88, 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]

(172−67, 172, 177)-Net over F₃ — Digital

Digital (105, 172, 177)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−67, 172, 1920)-Net in Base 3 — Upper bound on s

There is no (105, 172, 1921)-net in base 3, because

1 times m-reduction [i] would yield (105, 171, 1921)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3894 974730 902879 623651 521282 192577 473435 401544 226617 618815 841411 159511 564210 399875 > 3¹⁷¹ [i]