MinT - Best Known (129, 129+52, s)-Nets in Base 3

Best Known (129, 129+52, s)-Nets in Base 3

(129, 129+52, 252)-Net over F₃ — Constructive and digital

Digital (129, 181, 252)-net over F₃, using

3¹ times duplication [i] based on digital (128, 180, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 60, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(129, 129+52, 469)-Net over F₃ — Digital

Digital (129, 181, 469)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(129, 129+52, 11034)-Net in Base 3 — Upper bound on s

There is no (129, 181, 11035)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 228 707054 549599 468037 283975 634251 480356 882005 275631 028796 804384 949274 695888 196642 909925 > 3¹⁸¹ [i]