MinT - Best Known (108−30, 108, s)-Nets in Base 3

Best Known (108−30, 108, s)-Nets in Base 3

(108−30, 108, 228)-Net over F₃ — Constructive and digital

Digital (78, 108, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 36, 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]

(108−30, 108, 353)-Net over F₃ — Digital

Digital (78, 108, 353)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(108−30, 108, 8735)-Net in Base 3 — Upper bound on s

There is no (78, 108, 8736)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3384 043006 909505 231471 314074 573321 950044 299705 491841 > 3¹⁰⁸ [i]