MinT - Best Known (106, 106+44, s)-Nets in Base 3

Best Known (106, 106+44, s)-Nets in Base 3

(106, 106+44, 228)-Net over F₃ — Constructive and digital

Digital (106, 150, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 50, 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]

(106, 106+44, 374)-Net over F₃ — Digital

Digital (106, 150, 374)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 106+44, 8086)-Net in Base 3 — Upper bound on s

There is no (106, 150, 8087)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 370302 560511 633581 661164 377087 931320 914891 592615 112815 558804 586804 935749 > 3¹⁵⁰ [i]