MinT - Best Known (130, 130+67, s)-Nets in Base 3

Best Known (130, 130+67, s)-Nets in Base 3

(130, 130+67, 156)-Net over F₃ — Constructive and digital

Digital (130, 197, 156)-net over F₃, using

19 times m-reduction [i] based on digital (130, 216, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 108, 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]

(130, 130+67, 295)-Net over F₃ — Digital

Digital (130, 197, 295)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(130, 130+67, 4456)-Net in Base 3 — Upper bound on s

There is no (130, 197, 4457)-net in base 3, because

1 times m-reduction [i] would yield (130, 196, 4457)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3292 492844 593785 251184 730110 146862 837306 481623 414393 001195 788154 121116 460559 828888 820583 176275 > 3¹⁹⁶ [i]