MinT - Best Known (108−70, 108, s)-Nets in Base 9

Best Known (108−70, 108, s)-Nets in Base 9

(108−70, 108, 81)-Net over F₉ — Constructive and digital

Digital (38, 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]

(108−70, 108, 128)-Net over F₉ — Digital

Digital (38, 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]

(108−70, 108, 1508)-Net in Base 9 — Upper bound on s

There is no (38, 108, 1509)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11 507282 764204 616606 867478 331051 823740 122281 651347 949918 395743 271325 467960 050764 675411 636527 086411 754425 > 9¹⁰⁸ [i]