MinT - Best Known (162−69, 162, s)-Nets in Base 3

Best Known (162−69, 162, s)-Nets in Base 3

(162−69, 162, 80)-Net over F₃ — Constructive and digital

Digital (93, 162, 80)-net over F₃, using

8 times m-reduction [i] based on digital (93, 170, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 85, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(162−69, 162, 131)-Net over F₃ — Digital

Digital (93, 162, 131)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(162−69, 162, 1196)-Net in Base 3 — Upper bound on s

There is no (93, 162, 1197)-net in base 3, because

1 times m-reduction [i] would yield (93, 161, 1197)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 66546 464751 187173 290963 612943 605477 508595 370184 044046 909067 561573 588298 791009 > 3¹⁶¹ [i]