MinT - Best Known (98−69, 98, s)-Nets in Base 9

Best Known (98−69, 98, s)-Nets in Base 9

(98−69, 98, 78)-Net over F₉ — Constructive and digital

Digital (29, 98, 78)-net over F₉, using

t-expansion [i] based on digital (22, 98, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(98−69, 98, 110)-Net over F₉ — Digital

Digital (29, 98, 110)-net over F₉, using

t-expansion [i] based on digital (26, 98, 110)-net over F₉, using
- net from sequence [i] based on digital (26, 109)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 26 and N(F) ≥ 110, using
    - a curve from the manYPoints database [i]

(98−69, 98, 872)-Net in Base 9 — Upper bound on s

There is no (29, 98, 873)-net in base 9, because

1 times m-reduction [i] would yield (29, 97, 873)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 374 898449 775130 600887 836547 184617 584289 646097 510541 420065 517897 130788 097897 028124 549114 809041 > 9⁹⁷ [i]