MinT - Best Known (232−71, 232, s)-Nets in Base 3

Best Known (232−71, 232, s)-Nets in Base 3

(232−71, 232, 228)-Net over F₃ — Constructive and digital

Digital (161, 232, 228)-net over F₃, using

3¹ times duplication [i] based on digital (160, 231, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 77, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(232−71, 232, 474)-Net over F₃ — Digital

Digital (161, 232, 474)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(232−71, 232, 9765)-Net in Base 3 — Upper bound on s

There is no (161, 232, 9766)-net in base 3, because

1 times m-reduction [i] would yield (161, 231, 9766)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 164 220292 207720 672377 898288 796465 748713 657407 927472 534874 251777 563130 759887 370578 388381 016263 676651 298816 881441 > 3²³¹ [i]