MinT - Best Known (96, 96+51, s)-Nets in Base 3

Best Known (96, 96+51, s)-Nets in Base 3

(96, 96+51, 156)-Net over F₃ — Constructive and digital

Digital (96, 147, 156)-net over F₃, using

1 times m-reduction [i] based on digital (96, 148, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 74, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(96, 96+51, 218)-Net over F₃ — Digital

Digital (96, 147, 218)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(96, 96+51, 3087)-Net in Base 3 — Upper bound on s

There is no (96, 147, 3088)-net in base 3, because

1 times m-reduction [i] would yield (96, 146, 3088)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4597 885281 805169 327828 936508 599903 617241 427328 246259 653921 605543 273249 > 3¹⁴⁶ [i]