MinT - Best Known (28−13, 28, s)-Nets in Base 9

Best Known (28−13, 28, s)-Nets in Base 9

(28−13, 28, 200)-Net over F₉ — Constructive and digital

Digital (15, 28, 200)-net over F₉, using

trace code for nets [i] based on digital (1, 14, 100)-net over F₈₁, using
- net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]

(28−13, 28, 7362)-Net in Base 9 — Upper bound on s

There is no (15, 28, 7363)-net in base 9, because

1 times m-reduction [i] would yield (15, 27, 7363)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 58 168247 408161 884002 284305 > 9²⁷ [i]