MinT - Best Known (236−87, 236, s)-Nets in Base 3

Best Known (236−87, 236, s)-Nets in Base 3

(236−87, 236, 156)-Net over F₃ — Constructive and digital

Digital (149, 236, 156)-net over F₃, using

t-expansion [i] based on digital (147, 236, 156)-net over F₃, using
- 14 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]

(236−87, 236, 273)-Net over F₃ — Digital

Digital (149, 236, 273)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−87, 236, 3377)-Net in Base 3 — Upper bound on s

There is no (149, 236, 3378)-net in base 3, because

1 times m-reduction [i] would yield (149, 235, 3378)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13421 474819 492906 231936 192149 021899 053091 231038 432121 478126 458420 757931 047479 291132 304390 377215 232227 520010 006401 > 3²³⁵ [i]