MinT - Best Known (116−105, 116, s)-Nets in Base 9

Best Known (116−105, 116, s)-Nets in Base 9

(116−105, 116, 40)-Net over F₉ — Constructive and digital

Digital (11, 116, 40)-net over F₉, using

t-expansion [i] based on digital (8, 116, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(116−105, 116, 55)-Net over F₉ — Digital

Digital (11, 116, 55)-net over F₉, using

net from sequence [i] based on digital (11, 54)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 11 and N(F) ≥ 55, using
  - a curve from the manYPoints database [i]

(116−105, 116, 104)-Net in Base 9 — Upper bound on s

There is no (11, 116, 105)-net in base 9, because

21 times m-reduction [i] would yield (11, 95, 105)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(9⁹⁵, 105, S₉, 84), but
  - the linear programming bound shows that MÂ â‰¥ 1240 505866 046627 131068 555034 347769 450501 463301 708903 427699 923262 975474 963339 381628 644774 672768 499337 / 265 061875 > 9⁹⁵ [i]