MinT - Best Known (43, 43+99, s)-Nets in Base 9

Best Known (43, 43+99, s)-Nets in Base 9

(43, 43+99, 81)-Net over F₉ — Constructive and digital

Digital (43, 142, 81)-net over F₉, using

t-expansion [i] based on digital (32, 142, 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]

(43, 43+99, 147)-Net over F₉ — Digital

Digital (43, 142, 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]

(43, 43+99, 1300)-Net in Base 9 — Upper bound on s

There is no (43, 142, 1301)-net in base 9, because

1 times m-reduction [i] would yield (43, 141, 1301)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 355 523611 854497 493565 564105 125895 435031 198966 370779 806265 970037 010338 325539 684912 841829 570836 940520 935605 355010 407187 700389 669326 283305 > 9¹⁴¹ [i]