MinT - Best Known (135−88, 135, s)-Nets in Base 9

Best Known (135−88, 135, s)-Nets in Base 9

(135−88, 135, 81)-Net over F₉ — Constructive and digital

Digital (47, 135, 81)-net over F₉, using

t-expansion [i] based on digital (32, 135, 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]

(135−88, 135, 162)-Net over F₉ — Digital

Digital (47, 135, 162)-net over F₉, using

t-expansion [i] based on digital (46, 135, 162)-net over F₉, using
- net from sequence [i] based on digital (46, 161)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 46 and N(F) ≥ 162, using
    - a curve from the manYPoints database [i]

(135−88, 135, 1799)-Net in Base 9 — Upper bound on s

There is no (47, 135, 1800)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 670 872686 306517 425432 519160 522533 779060 008569 150874 411901 322031 629164 049875 397610 376300 634082 588394 770352 219681 099172 123076 152577 > 9¹³⁵ [i]