MinT - Best Known (108−74, 108, s)-Nets in Base 9

Best Known (108−74, 108, s)-Nets in Base 9

(108−74, 108, 81)-Net over F₉ — Constructive and digital

Digital (34, 108, 81)-net over F₉, using

t-expansion [i] based on digital (32, 108, 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]

(108−74, 108, 128)-Net over F₉ — Digital

Digital (34, 108, 128)-net over F₉, using

t-expansion [i] based on digital (33, 108, 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]

(108−74, 108, 1094)-Net in Base 9 — Upper bound on s

There is no (34, 108, 1095)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11 498087 740731 162675 777698 007478 453563 548324 728917 666746 441427 795889 933058 657715 913137 462737 929895 577625 > 9¹⁰⁸ [i]