MinT - Best Known (79, 140, s)-Nets in Base 3

Best Known (79, 140, s)-Nets in Base 3

(79, 140, 80)-Net over F₃ — Constructive and digital

Digital (79, 140, 80)-net over F₃, using

2 times m-reduction [i] based on digital (79, 142, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 71, 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]

(79, 140, 109)-Net over F₃ — Digital

Digital (79, 140, 109)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(79, 140, 949)-Net in Base 3 — Upper bound on s

There is no (79, 140, 950)-net in base 3, because

1 times m-reduction [i] would yield (79, 139, 950)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 150370 241418 512964 880182 992409 811889 252136 145159 506797 012143 796517 > 3¹³⁹ [i]