MinT - Best Known (125−86, 125, s)-Nets in Base 5

Best Known (125−86, 125, s)-Nets in Base 5

(125−86, 125, 78)-Net over F₅ — Constructive and digital

Digital (39, 125, 78)-net over F₅, using

t-expansion [i] based on digital (38, 125, 78)-net over F₅, using
- net from sequence [i] based on digital (38, 77)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
    - an explicitly constructive algebraic function field [i]

(125−86, 125, 423)-Net in Base 5 — Upper bound on s

There is no (39, 125, 424)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2519 890070 362081 801630 525202 607350 021884 114940 741665 344125 292783 241665 140697 981352 413601 > 5¹²⁵ [i]