MinT - Best Known (249−78, 249, s)-Nets in Base 3

Best Known (249−78, 249, s)-Nets in Base 3

(249−78, 249, 204)-Net over F₃ — Constructive and digital

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]

(249−78, 249, 468)-Net over F₃ — Digital

Digital (171, 249, 468)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−78, 249, 8524)-Net in Base 3 — Upper bound on s

There is no (171, 249, 8525)-net in base 3, because

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]