MinT - Best Known (33, 33+85, s)-Nets in Base 9

Best Known (33, 33+85, s)-Nets in Base 9

(33, 33+85, 81)-Net over F₉ — Constructive and digital

Digital (33, 118, 81)-net over F₉, using

t-expansion [i] based on digital (32, 118, 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]

(33, 33+85, 128)-Net over F₉ — Digital

Digital (33, 118, 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]

(33, 33+85, 914)-Net in Base 9 — Upper bound on s

There is no (33, 118, 915)-net in base 9, because

1 times m-reduction [i] would yield (33, 117, 915)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4613 719521 939034 774271 647597 768953 456822 027594 495656 374161 099532 643577 542217 727431 664328 714985 496038 622100 357745 > 9¹¹⁷ [i]