MinT - Best Known (135−95, 135, s)-Nets in Base 9

Best Known (135−95, 135, s)-Nets in Base 9

(135−95, 135, 81)-Net over F₉ — Constructive and digital

Digital (40, 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]

(135−95, 135, 140)-Net over F₉ — Digital

Digital (40, 135, 140)-net over F₉, using

t-expansion [i] based on digital (39, 135, 140)-net over F₉, using
- net from sequence [i] based on digital (39, 139)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 39 and N(F) ≥ 140, using
    - a curve from the manYPoints database [i]

(135−95, 135, 1178)-Net in Base 9 — Upper bound on s

There is no (40, 135, 1179)-net in base 9, because

1 times m-reduction [i] would yield (40, 134, 1179)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 76 597225 854208 992437 442301 717764 348301 659057 302038 913757 360687 684936 481827 159719 499799 756745 024001 689111 201111 013175 834957 341225 > 9¹³⁴ [i]