MinT - Best Known (91−80, 91, s)-Nets in Base 9

Best Known (91−80, 91, s)-Nets in Base 9

(91−80, 91, 40)-Net over F₉ — Constructive and digital

Digital (11, 91, 40)-net over F₉, using

t-expansion [i] based on digital (8, 91, 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]

(91−80, 91, 55)-Net over F₉ — Digital

Digital (11, 91, 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]

(91−80, 91, 107)-Net in Base 9 — Upper bound on s

There is no (11, 91, 108)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁹¹, 108, S₉, 80), but
- the linear programming bound shows that MÂ â‰¥ 455578 567373 817698 035102 930675 343729 239335 462212 364339 226877 822719 578221 226488 389564 641933 918907 527639 / 562 266190 229975 > 9⁹¹ [i]