MinT - Best Known (115−35, 115, s)-Nets in Base 3

Best Known (115−35, 115, s)-Nets in Base 3

(115−35, 115, 156)-Net over F₃ — Constructive and digital

Digital (80, 115, 156)-net over F₃, using

1 times m-reduction [i] based on digital (80, 116, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 58, 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]

(115−35, 115, 268)-Net over F₃ — Digital

Digital (80, 115, 268)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(115−35, 115, 5664)-Net in Base 3 — Upper bound on s

There is no (80, 115, 5665)-net in base 3, because

1 times m-reduction [i] would yield (80, 114, 5665)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 467667 065853 777694 976871 089403 550462 209851 298396 855811 > 3¹¹⁴ [i]