MinT - Best Known (171, 171+70, s)-Nets in Base 3

Best Known (171, 171+70, s)-Nets in Base 3

(171, 171+70, 282)-Net over F₃ — Constructive and digital

Digital (171, 241, 282)-net over F₃, using

3¹ times duplication [i] based on digital (170, 240, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 80, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(171, 171+70, 579)-Net over F₃ — Digital

Digital (171, 241, 579)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(171, 171+70, 13379)-Net in Base 3 — Upper bound on s

There is no (171, 241, 13380)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9 702472 084158 037192 784742 111938 426891 631964 844665 201746 431925 751296 220194 694297 295677 215904 175195 667593 004819 262257 > 3²⁴¹ [i]