MinT - Best Known (138−50, 138, s)-Nets in Base 5

Best Known (138−50, 138, s)-Nets in Base 5

(138−50, 138, 296)-Net over F₅ — Constructive and digital

Digital (88, 138, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 69, 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]

(138−50, 138, 435)-Net over F₅ — Digital

Digital (88, 138, 435)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−50, 138, 18342)-Net in Base 5 — Upper bound on s

There is no (88, 138, 18343)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2 873467 872001 752432 675952 023601 001353 312915 869235 074729 408941 994512 858975 998956 355432 389745 122877 > 5¹³⁸ [i]