MinT - Best Known (153, 153+97, s)-Nets in Base 3

Best Known (153, 153+97, s)-Nets in Base 3

(153, 153+97, 156)-Net over F₃ — Constructive and digital

Digital (153, 250, 156)-net over F₃, using

t-expansion [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]

(153, 153+97, 248)-Net over F₃ — Digital

Digital (153, 250, 248)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(153, 153+97, 2750)-Net in Base 3 — Upper bound on s

There is no (153, 250, 2751)-net in base 3, because

1 times m-reduction [i] would yield (153, 249, 2751)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 63894 351883 697994 385700 645730 748841 899471 329762 239840 595159 823090 978595 896491 927753 005908 481732 704670 389986 473858 308001 > 3²⁴⁹ [i]