MinT - Best Known (132−61, 132, s)-Nets in Base 5

Best Known (132−61, 132, s)-Nets in Base 5

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

Digital (71, 132, 132)-net over F₅, using

2 times m-reduction [i] based on digital (71, 134, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 67, 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]

(132−61, 132, 171)-Net over F₅ — Digital

Digital (71, 132, 171)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−61, 132, 3373)-Net in Base 5 — Upper bound on s

There is no (71, 132, 3374)-net in base 5, because

1 times m-reduction [i] would yield (71, 131, 3374)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 36 895623 049211 379950 863293 570480 762030 339948 581976 873357 533652 928573 568997 216514 477413 619521 > 5¹³¹ [i]