MinT - Best Known (173−67, 173, s)-Nets in Base 3

Best Known (173−67, 173, s)-Nets in Base 3

(173−67, 173, 148)-Net over F₃ — Constructive and digital

Digital (106, 173, 148)-net over F₃, using

5 times m-reduction [i] based on digital (106, 178, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 89, 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]

(173−67, 173, 181)-Net over F₃ — Digital

Digital (106, 173, 181)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−67, 173, 1986)-Net in Base 3 — Upper bound on s

There is no (106, 173, 1987)-net in base 3, because

1 times m-reduction [i] would yield (106, 172, 1987)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11663 109856 629168 591473 353409 523922 675906 186020 235260 737901 086967 311312 425150 826567 > 3¹⁷² [i]