MinT - Best Known (82, 82+51, s)-Nets in Base 9

Best Known (82, 82+51, s)-Nets in Base 9

(82, 82+51, 448)-Net over F₉ — Constructive and digital

Digital (82, 133, 448)-net over F₉, using

5 times m-reduction [i] based on digital (82, 138, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 69, 224)-net over F₈₁, using
  - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
      - a function field by SÃ©mirat [i]

(82, 82+51, 862)-Net over F₉ — Digital

Digital (82, 133, 862)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+51, 138959)-Net in Base 9 — Upper bound on s

There is no (82, 133, 138960)-net in base 9, because

1 times m-reduction [i] would yield (82, 132, 138960)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 912075 502138 719598 655097 359659 886657 409435 228698 252090 314406 205326 758853 974967 265208 244802 311861 984860 960371 763339 943121 652353 > 9¹³² [i]