MinT - Best Known (250−63, 250, s)-Nets in Base 3

Best Known (250−63, 250, s)-Nets in Base 3

(250−63, 250, 324)-Net over F₃ — Constructive and digital

Digital (187, 250, 324)-net over F₃, using

3¹ times duplication [i] based on digital (186, 249, 324)-net over F₃, using
- t-expansion [i] based on digital (184, 249, 324)-net over F₃, using
  - trace code for nets [i] based on digital (18, 83, 108)-net over F₂₇, using
    - net from sequence [i] based on digital (18, 107)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 18 and N(F) ≥ 108, using
        F₃ from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F₂₇ [i]

(250−63, 250, 992)-Net over F₃ — Digital

Digital (187, 250, 992)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−63, 250, 42174)-Net in Base 3 — Upper bound on s

There is no (187, 250, 42175)-net in base 3, because

1 times m-reduction [i] would yield (187, 249, 42175)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 63583 685678 347026 620934 315264 373156 813642 489715 691658 270966 155610 951979 269795 796334 154504 353796 645842 441217 690877 606595 > 3²⁴⁹ [i]