MinT - Best Known (98, 159, s)-Nets in Base 3

Best Known (98, 159, s)-Nets in Base 3

(98, 159, 148)-Net over F₃ — Constructive and digital

Digital (98, 159, 148)-net over F₃, using

3 times m-reduction [i] based on digital (98, 162, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 81, 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]

(98, 159, 173)-Net over F₃ — Digital

Digital (98, 159, 173)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 159, 1932)-Net in Base 3 — Upper bound on s

There is no (98, 159, 1933)-net in base 3, because

1 times m-reduction [i] would yield (98, 158, 1933)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2456 459191 020232 056712 249419 066364 422977 701649 985515 911786 164389 073189 992305 > 3¹⁵⁸ [i]