MinT - Best Known (250−77, 250, s)-Nets in Base 3

Best Known (250−77, 250, s)-Nets in Base 3

(250−77, 250, 228)-Net over F₃ — Constructive and digital

Digital (173, 250, 228)-net over F₃, using

3¹ times duplication [i] based on digital (172, 249, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 83, 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]

(250−77, 250, 497)-Net over F₃ — Digital

Digital (173, 250, 497)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−77, 250, 10012)-Net in Base 3 — Upper bound on s

There is no (173, 250, 10013)-net in base 3, because

1 times m-reduction [i] would yield (173, 249, 10013)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 63628 983636 084867 560099 759766 419208 071824 673949 242734 687245 843607 243132 974643 730258 050184 924956 518682 700838 516810 050481 > 3²⁴⁹ [i]