MinT - Best Known (121−77, 121, s)-Nets in Base 9

Best Known (121−77, 121, s)-Nets in Base 9

(121−77, 121, 81)-Net over F₉ — Constructive and digital

Digital (44, 121, 81)-net over F₉, using

t-expansion [i] based on digital (32, 121, 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]

(121−77, 121, 147)-Net over F₉ — Digital

Digital (44, 121, 147)-net over F₉, using

t-expansion [i] based on digital (43, 121, 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]

(121−77, 121, 1913)-Net in Base 9 — Upper bound on s

There is no (44, 121, 1914)-net in base 9, because

1 times m-reduction [i] would yield (44, 120, 1914)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 245328 378178 350927 632882 273586 487706 121412 127098 625250 961332 466208 926149 127760 673929 908968 085044 355376 766841 842977 > 9¹²⁰ [i]