MinT - Best Known (79, 79+63, s)-Nets in Base 9

Best Known (79, 79+63, s)-Nets in Base 9

(79, 79+63, 344)-Net over F₉ — Constructive and digital

Digital (79, 142, 344)-net over F₉, using

2 times m-reduction [i] based on digital (79, 144, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 72, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(79, 79+63, 452)-Net over F₉ — Digital

Digital (79, 142, 452)-net over F₉, using

trace code for nets [i] based on digital (8, 71, 226)-net over F₈₁, using
- net from sequence [i] based on digital (8, 225)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 8 and N(F) ≥ 226, using
    - a curve from the manYPoints database [i]

(79, 79+63, 33959)-Net in Base 9 — Upper bound on s

There is no (79, 142, 33960)-net in base 9, because

1 times m-reduction [i] would yield (79, 141, 33960)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 353 382850 104840 332841 945657 257108 320264 227389 874922 974752 446488 848539 649255 294543 601347 567116 169935 060452 929190 601015 533875 325301 284801 > 9¹⁴¹ [i]