MinT - Best Known (156, 249, s)-Nets in Base 3

Best Known (156, 249, s)-Nets in Base 3

(156, 249, 156)-Net over F₃ — Constructive and digital

Digital (156, 249, 156)-net over F₃, using

t-expansion [i] based on digital (147, 249, 156)-net over F₃, using
- 1 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]

(156, 249, 276)-Net over F₃ — Digital

Digital (156, 249, 276)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(156, 249, 3316)-Net in Base 3 — Upper bound on s

There is no (156, 249, 3317)-net in base 3, because

1 times m-reduction [i] would yield (156, 248, 3317)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21466 435596 586242 097200 327278 318771 990447 705442 562842 882178 204686 201682 311558 522348 217823 390314 093058 983591 652822 707265 > 3²⁴⁸ [i]