MinT - Best Known (245−76, 245, s)-Nets in Base 3

Best Known (245−76, 245, s)-Nets in Base 3

(245−76, 245, 204)-Net over F₃ — Constructive and digital

Digital (169, 245, 204)-net over F₃, using

1 times m-reduction [i] based on digital (169, 246, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 82, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(245−76, 245, 477)-Net over F₃ — Digital

Digital (169, 245, 477)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−76, 245, 8915)-Net in Base 3 — Upper bound on s

There is no (169, 245, 8916)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 787 456506 872982 041638 708019 814149 495513 481183 445854 070270 853490 785057 374558 165941 761740 214979 381399 052332 802269 579705 > 3²⁴⁵ [i]