MinT - Best Known (47, 47+98, s)-Nets in Base 9

Best Known (47, 47+98, s)-Nets in Base 9

(47, 47+98, 81)-Net over F₉ — Constructive and digital

Digital (47, 145, 81)-net over F₉, using

t-expansion [i] based on digital (32, 145, 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]

(47, 47+98, 162)-Net over F₉ — Digital

Digital (47, 145, 162)-net over F₉, using

t-expansion [i] based on digital (46, 145, 162)-net over F₉, using
- net from sequence [i] based on digital (46, 161)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 46 and N(F) ≥ 162, using
    - a curve from the manYPoints database [i]

(47, 47+98, 1562)-Net in Base 9 — Upper bound on s

There is no (47, 145, 1563)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 373223 544242 108429 102317 438061 341017 736449 507355 423094 748617 204675 370575 957856 436538 206912 826792 605961 350793 931574 952128 360902 603454 305625 > 9¹⁴⁵ [i]