MinT - Best Known (89−25, 89, s)-Nets in Base 5

Best Known (89−25, 89, s)-Nets in Base 5

(89−25, 89, 296)-Net over F₅ — Constructive and digital

Digital (64, 89, 296)-net over F₅, using

1 times m-reduction [i] based on digital (64, 90, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 45, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(89−25, 89, 970)-Net over F₅ — Digital

Digital (64, 89, 970)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−25, 89, 176628)-Net in Base 5 — Upper bound on s

There is no (64, 89, 176629)-net in base 5, because

1 times m-reduction [i] would yield (64, 88, 176629)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 32 313041 637442 749308 446955 564665 939641 899707 402474 357823 439825 > 5⁸⁸ [i]