MinT - Best Known (105−29, 105, s)-Nets in Base 3

Best Known (105−29, 105, s)-Nets in Base 3

(105−29, 105, 228)-Net over F₃ — Constructive and digital

Digital (76, 105, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 35, 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]

(105−29, 105, 354)-Net over F₃ — Digital

Digital (76, 105, 354)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−29, 105, 10573)-Net in Base 3 — Upper bound on s

There is no (76, 105, 10574)-net in base 3, because

1 times m-reduction [i] would yield (76, 104, 10574)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 41 794138 168089 921303 853875 685622 777713 596736 745493 > 3¹⁰⁴ [i]