MinT - Best Known (143−93, 143, s)-Nets in Base 9

Best Known (143−93, 143, s)-Nets in Base 9

(143−93, 143, 81)-Net over F₉ — Constructive and digital

Digital (50, 143, 81)-net over F₉, using

t-expansion [i] based on digital (32, 143, 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]

(143−93, 143, 182)-Net over F₉ — Digital

Digital (50, 143, 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]

(143−93, 143, 1957)-Net in Base 9 — Upper bound on s

There is no (50, 143, 1958)-net in base 9, because

1 times m-reduction [i] would yield (50, 142, 1958)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3235 585879 964008 564026 468615 244922 298311 968029 160031 784420 449505 698072 501907 109677 585289 852880 206027 196904 691921 919089 440591 021728 703585 > 9¹⁴² [i]