MinT - Best Known (81, 124, s)-Nets in Base 9

Best Known (81, 124, s)-Nets in Base 9

(81, 124, 740)-Net over F₉ — Constructive and digital

Digital (81, 124, 740)-net over F₉, using

6 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, 124, 1376)-Net over F₉ — Digital

Digital (81, 124, 1376)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 124, 421234)-Net in Base 9 — Upper bound on s

There is no (81, 124, 421235)-net in base 9, because

1 times m-reduction [i] would yield (81, 123, 421235)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2354 141615 383745 160431 653437 973410 980144 997697 216943 615852 245565 393912 763866 288633 522068 584458 333791 456878 415601 658489 > 9¹²³ [i]