MinT - Best Known (96−55, 96, s)-Nets in Base 9

Best Known (96−55, 96, s)-Nets in Base 9

(96−55, 96, 81)-Net over F₉ — Constructive and digital

Digital (41, 96, 81)-net over F₉, using

t-expansion [i] based on digital (32, 96, 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]

(96−55, 96, 88)-Net in Base 9 — Constructive

(41, 96, 88)-net in base 9, using

base change [i] based on digital (9, 64, 88)-net over F₂₇, using
- net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
    - a function field by SÃ©mirat [i]

(96−55, 96, 140)-Net over F₉ — Digital

Digital (41, 96, 140)-net over F₉, using

t-expansion [i] based on digital (39, 96, 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]

(96−55, 96, 3094)-Net in Base 9 — Upper bound on s

There is no (41, 96, 3095)-net in base 9, because

1 times m-reduction [i] would yield (41, 95, 3095)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 529645 213972 679961 166956 439228 805462 227487 444014 792001 498926 266282 598214 191568 190662 256233 > 9⁹⁵ [i]