MinT - Best Known (133−89, 133, s)-Nets in Base 9

Best Known (133−89, 133, s)-Nets in Base 9

(133−89, 133, 81)-Net over F₉ — Constructive and digital

Digital (44, 133, 81)-net over F₉, using

t-expansion [i] based on digital (32, 133, 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]

(133−89, 133, 147)-Net over F₉ — Digital

Digital (44, 133, 147)-net over F₉, using

t-expansion [i] based on digital (43, 133, 147)-net over F₉, using
- net from sequence [i] based on digital (43, 146)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
    - a curve from the manYPoints database [i]

(133−89, 133, 1545)-Net in Base 9 — Upper bound on s

There is no (44, 133, 1546)-net in base 9, because

1 times m-reduction [i] would yield (44, 132, 1546)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 924240 258510 336272 289653 204923 137050 455908 372146 797742 221581 085123 042395 158183 828909 854625 619876 653380 754879 213671 909281 402177 > 9¹³² [i]