MinT - Best Known (138−40, 138, s)-Nets in Base 3

Best Known (138−40, 138, s)-Nets in Base 3

(138−40, 138, 228)-Net over F₃ — Constructive and digital

Digital (98, 138, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 46, 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]

(138−40, 138, 365)-Net over F₃ — Digital

Digital (98, 138, 365)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−40, 138, 8116)-Net in Base 3 — Upper bound on s

There is no (98, 138, 8117)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 696958 665043 280338 207315 137660 779328 433067 647680 996084 550425 145233 > 3¹³⁸ [i]