MinT - Best Known (137−61, 137, s)-Nets in Base 5

Best Known (137−61, 137, s)-Nets in Base 5

(137−61, 137, 132)-Net over F₅ — Constructive and digital

Digital (76, 137, 132)-net over F₅, using

7 times m-reduction [i] based on digital (76, 144, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 72, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(137−61, 137, 201)-Net over F₅ — Digital

Digital (76, 137, 201)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−61, 137, 4418)-Net in Base 5 — Upper bound on s

There is no (76, 137, 4419)-net in base 5, because

1 times m-reduction [i] would yield (76, 136, 4419)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 115464 530429 477944 215218 708995 440501 229739 829755 837406 297439 826212 972799 356760 750748 916529 433993 > 5¹³⁶ [i]