MinT - Best Known (32, 53, s)-Nets in Base 9

Best Known (32, 53, s)-Nets in Base 9

Digital (32, 53, 320)-net over F₉, using

1 times m-reduction [i] based on digital (32, 54, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 27, 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]

Digital (32, 53, 362)-net over F₉, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(9⁵³, 362, F₉, 21) (dual of [362, 309, 22]-code), using
- 27 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (1, 26 times 0) [i] based on linear OA(9⁵², 334, F₉, 21) (dual of [334, 282, 22]-code), using
  - trace code [i] based on linear OA(81²⁶, 167, F₈₁, 21) (dual of [167, 141, 22]-code), using
    - extended algebraic-geometric code AG_e(F,145P) [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 167, using
      - a curve from the manYPoints database [i]

There is no (32, 53, 51868)-net in base 9, because

1 times m-reduction [i] would yield (32, 52, 51868)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 41 745846 016463 768539 522999 480181 988108 745496 074305 > 9⁵² [i]