MinT - Best Known (250−79, 250, s)-Nets in Base 3

Best Known (250−79, 250, s)-Nets in Base 3

(250−79, 250, 192)-Net over F₃ — Constructive and digital

Digital (171, 250, 192)-net over F₃, using

3¹ times duplication [i] based on digital (170, 249, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 83, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(250−79, 250, 457)-Net over F₃ — Digital

Digital (171, 250, 457)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−79, 250, 8524)-Net in Base 3 — Upper bound on s

There is no (171, 250, 8525)-net in base 3, because

1 times m-reduction [i] would yield (171, 249, 8525)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 63656 523140 125416 773908 475077 965938 632048 670293 694911 177531 709659 313287 065567 815603 934066 234657 873604 194064 993847 796603 > 3²⁴⁹ [i]