MinT - Best Known (127−81, 127, s)-Nets in Base 9

Best Known (127−81, 127, s)-Nets in Base 9

(127−81, 127, 81)-Net over F₉ — Constructive and digital

Digital (46, 127, 81)-net over F₉, using

t-expansion [i] based on digital (32, 127, 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]

(127−81, 127, 162)-Net over F₉ — Digital

Digital (46, 127, 162)-net over F₉, using

net from sequence [i] based on digital (46, 161)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 46 and N(F) ≥ 162, using
  - a curve from the manYPoints database [i]

(127−81, 127, 1973)-Net in Base 9 — Upper bound on s

There is no (46, 127, 1974)-net in base 9, because

1 times m-reduction [i] would yield (46, 126, 1974)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 735231 165161 195509 608426 700742 299427 226763 124709 300256 092876 163976 701724 363409 892117 576273 734991 784246 496832 133443 111553 > 9¹²⁶ [i]