MinT - Best Known (52, 52+42, s)-Nets in Base 9

Best Known (52, 52+42, s)-Nets in Base 9

(52, 52+42, 320)-Net over F₉ — Constructive and digital

Digital (52, 94, 320)-net over F₉, using

trace code for nets [i] based on digital (5, 47, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(52, 52+42, 334)-Net over F₉ — Digital

Digital (52, 94, 334)-net over F₉, using

trace code for nets [i] based on digital (5, 47, 167)-net over F₈₁, using
- net from sequence [i] based on digital (5, 166)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 167, using
    - a curve from the manYPoints database [i]

(52, 52+42, 20253)-Net in Base 9 — Upper bound on s

There is no (52, 94, 20254)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 499982 516255 749308 401788 801336 205616 252448 471643 320137 128834 630675 695652 209632 746512 123953 > 9⁹⁴ [i]