MinT - Best Known (135−100, 135, s)-Nets in Base 9

Best Known (135−100, 135, s)-Nets in Base 9

(135−100, 135, 81)-Net over F₉ — Constructive and digital

Digital (35, 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]

(135−100, 135, 128)-Net over F₉ — Digital

Digital (35, 135, 128)-net over F₉, using

t-expansion [i] based on digital (33, 135, 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]

(135−100, 135, 887)-Net in Base 9 — Upper bound on s

There is no (35, 135, 888)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 667 224787 393225 570946 097336 728043 531047 063042 826334 353273 054328 076471 729534 158155 752306 336029 711530 012624 607758 502734 856691 866241 > 9¹³⁵ [i]