MinT - Best Known (248−77, 248, s)-Nets in Base 3

Best Known (248−77, 248, s)-Nets in Base 3

(248−77, 248, 204)-Net over F₃ — Constructive and digital

Digital (171, 248, 204)-net over F₃, using

1 times m-reduction [i] based on digital (171, 249, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 83, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(248−77, 248, 480)-Net over F₃ — Digital

Digital (171, 248, 480)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−77, 248, 9448)-Net in Base 3 — Upper bound on s

There is no (171, 248, 9449)-net in base 3, because

1 times m-reduction [i] would yield (171, 247, 9449)-net in base 3, but
- 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]