MinT - Best Known (133−99, 133, s)-Nets in Base 9

Best Known (133−99, 133, s)-Nets in Base 9

(133−99, 133, 81)-Net over F₉ — Constructive and digital

Digital (34, 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]

(133−99, 133, 128)-Net over F₉ — Digital

Digital (34, 133, 128)-net over F₉, using

t-expansion [i] based on digital (33, 133, 128)-net over F₉, using
- net from sequence [i] based on digital (33, 127)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
    - a curve from the manYPoints database [i]

(133−99, 133, 859)-Net in Base 9 — Upper bound on s

There is no (34, 133, 860)-net in base 9, because

1 times m-reduction [i] would yield (34, 132, 860)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 962425 949637 129293 763895 261947 907083 178299 180963 669476 404308 709234 821688 833069 295143 045323 462045 644123 602659 212169 424264 341729 > 9¹³² [i]