MinT - Best Known (103, 103+29, s)-Nets in Base 5

Best Known (103, 103+29, s)-Nets in Base 5

(103, 103+29, 504)-Net over F₅ — Constructive and digital

Digital (103, 132, 504)-net over F₅, using

t-expansion [i] based on digital (101, 132, 504)-net over F₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (35, 50, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 25, 126)-net over F₂₅, using
      - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
        the Hermitian function field over F₂₅ [i]
  2. digital (51, 82, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 41, 126)-net over F₂₅, using
      - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(103, 103+29, 5587)-Net over F₅ — Digital

Digital (103, 132, 5587)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(103, 103+29, 5245164)-Net in Base 5 — Upper bound on s

There is no (103, 132, 5245165)-net in base 5, because

1 times m-reduction [i] would yield (103, 131, 5245165)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 36 734258 897316 230962 483919 035793 088273 931915 743807 698261 743857 554144 186664 734624 331984 681321 > 5¹³¹ [i]