MinT - Best Known (41, 99, s)-Nets in Base 9

Best Known (41, 99, s)-Nets in Base 9

(41, 99, 81)-Net over F₉ — Constructive and digital

Digital (41, 99, 81)-net over F₉, using

t-expansion [i] based on digital (32, 99, 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]

(41, 99, 84)-Net in Base 9 — Constructive

(41, 99, 84)-net in base 9, using

base change [i] based on digital (8, 66, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(41, 99, 140)-Net over F₉ — Digital

Digital (41, 99, 140)-net over F₉, using

t-expansion [i] based on digital (39, 99, 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]

(41, 99, 2622)-Net in Base 9 — Upper bound on s

There is no (41, 99, 2623)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 29675 639283 862151 902162 720310 283835 102736 770437 969335 170192 905883 714379 609109 247965 812330 567961 > 9⁹⁹ [i]