MinT - Best Known (233−99, 233, s)-Nets in Base 3

Best Known (233−99, 233, s)-Nets in Base 3

(233−99, 233, 148)-Net over F₃ — Constructive and digital

Digital (134, 233, 148)-net over F₃, using

1 times m-reduction [i] based on digital (134, 234, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 117, 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]

(233−99, 233, 180)-Net over F₃ — Digital

Digital (134, 233, 180)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(233−99, 233, 1687)-Net in Base 3 — Upper bound on s

There is no (134, 233, 1688)-net in base 3, because

1 times m-reduction [i] would yield (134, 232, 1688)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 505 365296 571897 346215 316077 156609 387600 269372 070488 702743 353907 714996 880863 006538 466570 151033 685215 299958 757937 > 3²³² [i]