MinT - Best Known (236−95, 236, s)-Nets in Base 3

Best Known (236−95, 236, s)-Nets in Base 3

(236−95, 236, 156)-Net over F₃ — Constructive and digital

Digital (141, 236, 156)-net over F₃, using

2 times m-reduction [i] based on digital (141, 238, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 119, 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]

(236−95, 236, 212)-Net over F₃ — Digital

Digital (141, 236, 212)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−95, 236, 2185)-Net in Base 3 — Upper bound on s

There is no (141, 236, 2186)-net in base 3, because

1 times m-reduction [i] would yield (141, 235, 2186)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13344 024112 254196 172201 194203 354273 480554 514970 968534 966337 361098 113552 153851 478039 996685 839607 882964 746534 704057 > 3²³⁵ [i]