MinT - Best Known (57, 147, s)-Nets in Base 9

Best Known (57, 147, s)-Nets in Base 9

(57, 147, 81)-Net over F₉ — Constructive and digital

Digital (57, 147, 81)-net over F₉, using

t-expansion [i] based on digital (32, 147, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(57, 147, 84)-Net in Base 9 — Constructive

(57, 147, 84)-net in base 9, using

base change [i] based on digital (8, 98, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(57, 147, 182)-Net over F₉ — Digital

Digital (57, 147, 182)-net over F₉, using

t-expansion [i] based on digital (50, 147, 182)-net over F₉, using
- net from sequence [i] based on digital (50, 181)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 50 and N(F) ≥ 182, using
    - a curve from the manYPoints database [i]

(57, 147, 2858)-Net in Base 9 — Upper bound on s

There is no (57, 147, 2859)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 189 793707 572517 169837 364674 911973 508927 479936 759691 871027 656300 151941 493018 582035 071942 969564 420843 255135 352795 112368 604565 354825 236285 440889 > 9¹⁴⁷ [i]