MinT - Best Known (158−61, 158, s)-Nets in Base 3

Best Known (158−61, 158, s)-Nets in Base 3

(158−61, 158, 148)-Net over F₃ — Constructive and digital

Digital (97, 158, 148)-net over F₃, using

2 times m-reduction [i] based on digital (97, 160, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 80, 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]

(158−61, 158, 169)-Net over F₃ — Digital

Digital (97, 158, 169)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(158−61, 158, 1861)-Net in Base 3 — Upper bound on s

There is no (97, 158, 1862)-net in base 3, because

1 times m-reduction [i] would yield (97, 157, 1862)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 813 049589 302150 539514 689099 781245 172555 415855 426535 661367 326945 847895 139717 > 3¹⁵⁷ [i]