MinT - Best Known (49−30, 49, s)-Nets in Base 9

Best Known (49−30, 49, s)-Nets in Base 9

(49−30, 49, 74)-Net over F₉ — Constructive and digital

Digital (19, 49, 74)-net over F₉, using

t-expansion [i] based on digital (17, 49, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(49−30, 49, 84)-Net over F₉ — Digital

Digital (19, 49, 84)-net over F₉, using

net from sequence [i] based on digital (19, 83)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 19 and N(F) ≥ 84, using
  - Drinfeld modules of rank 1 [i]

(49−30, 49, 1042)-Net in Base 9 — Upper bound on s

There is no (19, 49, 1043)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 57434 222400 125966 813295 144593 278062 908990 492777 > 9⁴⁹ [i]