MinT - Best Known (175, 175+73, s)-Nets in Base 3

Best Known (175, 175+73, s)-Nets in Base 3

(175, 175+73, 264)-Net over F₃ — Constructive and digital

Digital (175, 248, 264)-net over F₃, using

1 times m-reduction [i] based on digital (175, 249, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 83, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(175, 175+73, 569)-Net over F₃ — Digital

Digital (175, 248, 569)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(175, 175+73, 13370)-Net in Base 3 — Upper bound on s

There is no (175, 248, 13371)-net in base 3, because

1 times m-reduction [i] would yield (175, 247, 13371)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7077 075347 707045 972380 821115 095933 163361 573348 410095 264636 319671 854657 025061 576363 854368 449441 863234 329172 602533 239193 > 3²⁴⁷ [i]