MinT - Best Known (43, 43+105, s)-Nets in Base 9

Best Known (43, 43+105, s)-Nets in Base 9

(43, 43+105, 81)-Net over F₉ — Constructive and digital

Digital (43, 148, 81)-net over F₉, using

t-expansion [i] based on digital (32, 148, 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]

(43, 43+105, 147)-Net over F₉ — Digital

Digital (43, 148, 147)-net over F₉, using

net from sequence [i] based on digital (43, 146)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
  - a curve from the manYPoints database [i]

(43, 43+105, 1228)-Net in Base 9 — Upper bound on s

There is no (43, 148, 1229)-net in base 9, because

1 times m-reduction [i] would yield (43, 147, 1229)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 193 646318 495544 514403 848214 702008 051483 048487 190790 821467 476336 606683 966132 862418 940700 369154 805207 351631 084006 007215 954618 272481 140938 009505 > 9¹⁴⁷ [i]