MinT - Best Known (233−85, 233, s)-Nets in Base 3

Best Known (233−85, 233, s)-Nets in Base 3

(233−85, 233, 156)-Net over F₃ — Constructive and digital

Digital (148, 233, 156)-net over F₃, using

t-expansion [i] based on digital (147, 233, 156)-net over F₃, using
- 17 times m-reduction [i] based on digital (147, 250, 156)-net over F₃, using
  - trace code for nets [i] based on digital (22, 125, 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]

(233−85, 233, 278)-Net over F₃ — Digital

Digital (148, 233, 278)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(233−85, 233, 3525)-Net in Base 3 — Upper bound on s

There is no (148, 233, 3526)-net in base 3, because

1 times m-reduction [i] would yield (148, 232, 3526)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 494 134099 080879 999968 032972 599019 983845 179892 234415 136837 862611 154342 034464 484686 311921 835270 195324 519026 936765 > 3²³² [i]