MinT - Best Known (89−35, 89, s)-Nets in Base 5

Best Known (89−35, 89, s)-Nets in Base 5

(89−35, 89, 208)-Net over F₅ — Constructive and digital

Digital (54, 89, 208)-net over F₅, using

1 times m-reduction [i] based on digital (54, 90, 208)-net over F₅, using
- trace code for nets [i] based on digital (9, 45, 104)-net over F₂₅, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by GarcÃa and Quoos [i]

(89−35, 89, 222)-Net over F₅ — Digital

Digital (54, 89, 222)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−35, 89, 7436)-Net in Base 5 — Upper bound on s

There is no (54, 89, 7437)-net in base 5, because

1 times m-reduction [i] would yield (54, 88, 7437)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 32 348744 937465 452978 637393 884741 541551 490548 968885 782882 235125 > 5⁸⁸ [i]