MinT - Best Known (87−23, 87, s)-Nets in Base 5

Best Known (87−23, 87, s)-Nets in Base 5

(87−23, 87, 296)-Net over F₅ — Constructive and digital

Digital (64, 87, 296)-net over F₅, using

3 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]

(87−23, 87, 1326)-Net over F₅ — Digital

Digital (64, 87, 1326)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(87−23, 87, 357782)-Net in Base 5 — Upper bound on s

There is no (64, 87, 357783)-net in base 5, because

1 times m-reduction [i] would yield (64, 86, 357783)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 292481 630728 603440 699171 657800 354909 940934 197503 986414 251445 > 5⁸⁶ [i]