MinT - Best Known (42, 42+100, s)-Nets in Base 9

Best Known (42, 42+100, s)-Nets in Base 9

(42, 42+100, 81)-Net over F₉ — Constructive and digital

Digital (42, 142, 81)-net over F₉, using

t-expansion [i] based on digital (32, 142, 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]

(42, 42+100, 140)-Net over F₉ — Digital

Digital (42, 142, 140)-net over F₉, using

t-expansion [i] based on digital (39, 142, 140)-net over F₉, using
- net from sequence [i] based on digital (39, 139)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 39 and N(F) ≥ 140, using
    - a curve from the manYPoints database [i]

(42, 42+100, 1218)-Net in Base 9 — Upper bound on s

There is no (42, 142, 1219)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3226 826438 681778 259581 938277 120895 996008 392068 852081 515657 462944 736870 321567 859978 715434 223906 571862 748304 528544 057984 885755 922415 453745 > 9¹⁴² [i]