MinT - Best Known (81, 127, s)-Nets in Base 9

Best Known (81, 127, s)-Nets in Base 9

(81, 127, 740)-Net over F₉ — Constructive and digital

Digital (81, 127, 740)-net over F₉, using

3 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, 127, 1109)-Net over F₉ — Digital

Digital (81, 127, 1109)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 127, 218986)-Net in Base 9 — Upper bound on s

There is no (81, 127, 218987)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15 446490 124655 419291 406348 482434 988792 597640 051059 327371 479344 463811 976223 004568 562980 757407 886941 578422 656925 254208 564073 > 9¹²⁷ [i]