MinT - Best Known (44, 137, s)-Nets in Base 9

Best Known (44, 137, s)-Nets in Base 9

(44, 137, 81)-Net over F₉ — Constructive and digital

Digital (44, 137, 81)-net over F₉, using

t-expansion [i] based on digital (32, 137, 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, 137, 147)-Net over F₉ — Digital

Digital (44, 137, 147)-net over F₉, using

t-expansion [i] based on digital (43, 137, 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, 137, 1462)-Net in Base 9 — Upper bound on s

There is no (44, 137, 1463)-net in base 9, because

1 times m-reduction [i] would yield (44, 136, 1463)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6064 667982 981814 254120 582538 517160 120398 850421 997725 921333 858166 391419 440489 802275 861569 298343 503221 745709 281324 954705 666429 301265 > 9¹³⁶ [i]