MinT - Best Known (102, 144, s)-Nets in Base 3

Best Known (102, 144, s)-Nets in Base 3

(102, 144, 228)-Net over F₃ — Constructive and digital

Digital (102, 144, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 48, 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]

(102, 144, 369)-Net over F₃ — Digital

Digital (102, 144, 369)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 144, 8091)-Net in Base 3 — Upper bound on s

There is no (102, 144, 8092)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 507 587093 379800 825420 129959 101887 631344 282748 407292 177727 847215 339545 > 3¹⁴⁴ [i]