MinT - Best Known (51, 148, s)-Nets in Base 9

Best Known (51, 148, s)-Nets in Base 9

(51, 148, 81)-Net over F₉ — Constructive and digital

Digital (51, 148, 81)-net over F₉, using

t-expansion [i] based on digital (32, 148, 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]

(51, 148, 182)-Net over F₉ — Digital

Digital (51, 148, 182)-net over F₉, using

t-expansion [i] based on digital (50, 148, 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]

(51, 148, 1929)-Net in Base 9 — Upper bound on s

There is no (51, 148, 1930)-net in base 9, because

1 times m-reduction [i] would yield (51, 147, 1930)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 188 803238 168333 233063 063159 130542 673299 666718 245663 319795 427202 565430 595297 933487 329827 234351 314274 752480 889864 366369 170417 251304 497304 347905 > 9¹⁴⁷ [i]