MinT - Best Known (175−75, 175, s)-Nets in Base 3

Best Known (175−75, 175, s)-Nets in Base 3

(175−75, 175, 80)-Net over F₃ — Constructive and digital

Digital (100, 175, 80)-net over F₃, using

9 times m-reduction [i] based on digital (100, 184, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 92, 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]

(175−75, 175, 137)-Net over F₃ — Digital

Digital (100, 175, 137)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(175−75, 175, 1248)-Net in Base 3 — Upper bound on s

There is no (100, 175, 1249)-net in base 3, because

1 times m-reduction [i] would yield (100, 174, 1249)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 107080 836749 434713 329712 791229 066109 149929 007070 003957 513673 683833 120246 244724 568627 > 3¹⁷⁴ [i]