MinT - Best Known (171, 171+74, s)-Nets in Base 3

Best Known (171, 171+74, s)-Nets in Base 3

(171, 171+74, 246)-Net over F₃ — Constructive and digital

Digital (171, 245, 246)-net over F₃, using

1 times m-reduction [i] based on digital (171, 246, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 82, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(171, 171+74, 518)-Net over F₃ — Digital

Digital (171, 245, 518)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(171, 171+74, 10536)-Net in Base 3 — Upper bound on s

There is no (171, 245, 10537)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 785 936781 087947 558030 832825 763869 488154 579439 776660 329707 514290 987450 899028 638059 603974 140014 565572 422333 065655 628355 > 3²⁴⁵ [i]