MinT - Best Known (102−28, 102, s)-Nets in Base 3

Best Known (102−28, 102, s)-Nets in Base 3

(102−28, 102, 228)-Net over F₃ — Constructive and digital

Digital (74, 102, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 34, 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]

(102−28, 102, 355)-Net over F₃ — Digital

Digital (74, 102, 355)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(102−28, 102, 9035)-Net in Base 3 — Upper bound on s

There is no (74, 102, 9036)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 642480 652465 155914 398152 139686 304285 671411 132937 > 3¹⁰² [i]