MinT - Best Known (129, 129+53, s)-Nets in Base 3

Best Known (129, 129+53, s)-Nets in Base 3

(129, 129+53, 246)-Net over F₃ — Constructive and digital

Digital (129, 182, 246)-net over F₃, using

1 times m-reduction [i] based on digital (129, 183, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 61, 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]

(129, 129+53, 450)-Net over F₃ — Digital

Digital (129, 182, 450)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(129, 129+53, 11034)-Net in Base 3 — Upper bound on s

There is no (129, 182, 11035)-net in base 3, because

1 times m-reduction [i] would yield (129, 181, 11035)-net in base 3, but
- 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]