MinT - Best Known (81, 81+38, s)-Nets in Base 9

Best Known (81, 81+38, s)-Nets in Base 9

(81, 81+38, 740)-Net over F₉ — Constructive and digital

Digital (81, 119, 740)-net over F₉, using

11 times m-reduction [i] based on digital (81, 130, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 65, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(81, 81+38, 2166)-Net over F₉ — Digital

Digital (81, 119, 2166)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 81+38, 939056)-Net in Base 9 — Upper bound on s

There is no (81, 119, 939057)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 358808 082528 367414 267195 211860 419904 718735 402549 468281 290707 404200 291978 097625 089293 413593 974381 866776 125055 307737 > 9¹¹⁹ [i]