MinT - Best Known (132−47, 132, s)-Nets in Base 5

Best Known (132−47, 132, s)-Nets in Base 5

(132−47, 132, 296)-Net over F₅ — Constructive and digital

Digital (85, 132, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 66, 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]

(132−47, 132, 450)-Net over F₅ — Digital

Digital (85, 132, 450)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−47, 132, 22550)-Net in Base 5 — Upper bound on s

There is no (85, 132, 22551)-net in base 5, because

1 times m-reduction [i] would yield (85, 131, 22551)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 36 737823 262826 754619 981479 661607 678451 102489 359099 490704 911796 162061 057774 147529 233612 315525 > 5¹³¹ [i]