MinT - Best Known (137−47, 137, s)-Nets in Base 5

Best Known (137−47, 137, s)-Nets in Base 5

(137−47, 137, 296)-Net over F₅ — Constructive and digital

Digital (90, 137, 296)-net over F₅, using

5 times m-reduction [i] based on digital (90, 142, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 71, 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]

(137−47, 137, 543)-Net over F₅ — Digital

Digital (90, 137, 543)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−47, 137, 32004)-Net in Base 5 — Upper bound on s

There is no (90, 137, 32005)-net in base 5, because

1 times m-reduction [i] would yield (90, 136, 32005)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 114847 309933 498916 386144 610281 655456 677843 602869 708558 009362 513465 050184 678094 712774 312163 294525 > 5¹³⁶ [i]