MinT - Best Known (88−25, 88, s)-Nets in Base 9

Best Known (88−25, 88, s)-Nets in Base 9

(88−25, 88, 740)-Net over F₉ — Constructive and digital

Digital (63, 88, 740)-net over F₉, using

6 times m-reduction [i] based on digital (63, 94, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 47, 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]

(88−25, 88, 3877)-Net over F₉ — Digital

Digital (63, 88, 3877)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−25, 88, 5476827)-Net in Base 9 — Upper bound on s

There is no (63, 88, 5476828)-net in base 9, because

1 times m-reduction [i] would yield (63, 87, 5476828)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 104495 783357 055583 274449 134573 256353 766656 292863 639230 172263 877347 469326 198420 364673 > 9⁸⁷ [i]