MinT - Best Known (44, 44+99, s)-Nets in Base 9

Best Known (44, 44+99, s)-Nets in Base 9

(44, 44+99, 81)-Net over F₉ — Constructive and digital

Digital (44, 143, 81)-net over F₉, using

t-expansion [i] based on digital (32, 143, 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]

(44, 44+99, 147)-Net over F₉ — Digital

Digital (44, 143, 147)-net over F₉, using

t-expansion [i] based on digital (43, 143, 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]

(44, 44+99, 1361)-Net in Base 9 — Upper bound on s

There is no (44, 143, 1362)-net in base 9, because

1 times m-reduction [i] would yield (44, 142, 1362)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3196 306443 720038 154982 515026 594623 997826 698878 054830 385387 385869 306772 785142 708544 763290 334850 284662 527030 983869 897323 506259 744349 112209 > 9¹⁴² [i]