MinT - Best Known (27−14, 27, s)-Nets in Base 9

Best Known (27−14, 27, s)-Nets in Base 9

(27−14, 27, 82)-Net over F₉ — Constructive and digital

Digital (13, 27, 82)-net over F₉, using

base reduction for projective spaces (embedding PG(13,81) in PG(26,9)) for nets [i] based on digital (0, 14, 82)-net over F₈₁, using
- net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
    - the rational function field F₈₁(x) [i]
  - Niederreiter sequence [i]

(27−14, 27, 2021)-Net in Base 9 — Upper bound on s

There is no (13, 27, 2022)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 58 275260 254178 046703 539345 > 9²⁷ [i]