MinT - Best Known (120−73, 120, s)-Nets in Base 9

Best Known (120−73, 120, s)-Nets in Base 9

(120−73, 120, 81)-Net over F₉ — Constructive and digital

Digital (47, 120, 81)-net over F₉, using

t-expansion [i] based on digital (32, 120, 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]

(120−73, 120, 82)-Net in Base 9 — Constructive

(47, 120, 82)-net in base 9, using

base change [i] based on digital (7, 80, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(120−73, 120, 162)-Net over F₉ — Digital

Digital (47, 120, 162)-net over F₉, using

t-expansion [i] based on digital (46, 120, 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]

(120−73, 120, 2524)-Net in Base 9 — Upper bound on s

There is no (47, 120, 2525)-net in base 9, because

1 times m-reduction [i] would yield (47, 119, 2525)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 360914 232628 950119 360238 354034 568249 162786 902545 746873 549735 160940 497972 298247 714594 586010 675764 712068 655329 567009 > 9¹¹⁹ [i]