MinT - Best Known (52, 52+46, s)-Nets in Base 9

Best Known (52, 52+46, s)-Nets in Base 9

(52, 52+46, 232)-Net over F₉ — Constructive and digital

Digital (52, 98, 232)-net over F₉, using

2 times m-reduction [i] based on digital (52, 100, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 50, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(52, 52+46, 272)-Net over F₉ — Digital

Digital (52, 98, 272)-net over F₉, using

trace code for nets [i] based on digital (3, 49, 136)-net over F₈₁, using
- net from sequence [i] based on digital (3, 135)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 3 and N(F) ≥ 136, using
    - a curve from the manYPoints database [i]

(52, 52+46, 13703)-Net in Base 9 — Upper bound on s

There is no (52, 98, 13704)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3282 234181 966894 509017 556600 650165 866193 285229 176074 029425 115563 388210 076426 103673 328072 523457 > 9⁹⁸ [i]