MinT - Best Known (238−97, 238, s)-Nets in Base 3

Best Known (238−97, 238, s)-Nets in Base 3

(238−97, 238, 156)-Net over F₃ — Constructive and digital

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]

(238−97, 238, 206)-Net over F₃ — Digital

Digital (141, 238, 206)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−97, 238, 2078)-Net in Base 3 — Upper bound on s

There is no (141, 238, 2079)-net in base 3, because

1 times m-reduction [i] would yield (141, 237, 2079)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 119999 912655 490733 135556 032006 041760 294500 285678 600520 842254 077074 650128 798932 629214 002923 395970 390657 026959 999905 > 3²³⁷ [i]