MinT - Best Known (171, 171+76, s)-Nets in Base 3

Best Known (171, 171+76, s)-Nets in Base 3

(171, 171+76, 228)-Net over F₃ — Constructive and digital

Digital (171, 247, 228)-net over F₃, using

3¹ times duplication [i] based on digital (170, 246, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 82, 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]

(171, 171+76, 493)-Net over F₃ — Digital

Digital (171, 247, 493)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(171, 171+76, 9448)-Net in Base 3 — Upper bound on s

There is no (171, 247, 9449)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7088 271016 097195 964942 334481 153734 373751 131988 842574 779883 853444 899746 333077 327752 837846 301916 320002 688946 385638 910825 > 3²⁴⁷ [i]