MinT - Best Known (250−75, 250, s)-Nets in Base 3

Best Known (250−75, 250, s)-Nets in Base 3

(250−75, 250, 252)-Net over F₃ — Constructive and digital

Digital (175, 250, 252)-net over F₃, using

3¹ times duplication [i] based on digital (174, 249, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 83, 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]

(250−75, 250, 539)-Net over F₃ — Digital

Digital (175, 250, 539)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−75, 250, 11869)-Net in Base 3 — Upper bound on s

There is no (175, 250, 11870)-net in base 3, because

1 times m-reduction [i] would yield (175, 249, 11870)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 63580 260234 964283 716485 600720 932967 976283 654301 855868 719065 825928 054517 141921 014592 674181 314225 772772 778667 017099 149717 > 3²⁴⁹ [i]