MinT - Best Known (10, 10+38, s)-Nets in Base 9

Best Known (10, 10+38, s)-Nets in Base 9

(10, 10+38, 40)-Net over F₉ — Constructive and digital

Digital (10, 48, 40)-net over F₉, using

t-expansion [i] based on digital (8, 48, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(10, 10+38, 54)-Net over F₉ — Digital

Digital (10, 48, 54)-net over F₉, using

net from sequence [i] based on digital (10, 53)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 10 and N(F) ≥ 54, using
  - a curve from the manYPoints database [i]

(10, 10+38, 243)-Net in Base 9 — Upper bound on s

There is no (10, 48, 244)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6384 706623 391253 788310 890992 163447 773308 796513 > 9⁴⁸ [i]