MinT - Best Known (162−71, 162, s)-Nets in Base 3

Best Known (162−71, 162, s)-Nets in Base 3

(162−71, 162, 80)-Net over F₃ — Constructive and digital

Digital (91, 162, 80)-net over F₃, using

4 times m-reduction [i] based on digital (91, 166, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 83, 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]

(162−71, 162, 121)-Net over F₃ — Digital

Digital (91, 162, 121)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(162−71, 162, 1054)-Net in Base 3 — Upper bound on s

There is no (91, 162, 1055)-net in base 3, because

1 times m-reduction [i] would yield (91, 161, 1055)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 65843 207094 719460 795619 698681 285016 825045 000220 007101 775562 823389 804615 842363 > 3¹⁶¹ [i]