MinT - Best Known (173, 173+49, s)-Nets in Base 3

Best Known (173, 173+49, s)-Nets in Base 3

(173, 173+49, 640)-Net over F₃ — Constructive and digital

Digital (173, 222, 640)-net over F₃, using

2 times m-reduction [i] based on digital (173, 224, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 56, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(173, 173+49, 1532)-Net over F₃ — Digital

Digital (173, 222, 1532)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(173, 173+49, 121266)-Net in Base 3 — Upper bound on s

There is no (173, 222, 121267)-net in base 3, because

1 times m-reduction [i] would yield (173, 221, 121267)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2778 797726 588073 289055 527027 163728 688665 225450 570047 815907 413435 418381 408141 783281 681657 961974 216199 784401 > 3²²¹ [i]