MinT - Best Known (106, 138, s)-Nets in Base 5

Best Known (106, 138, s)-Nets in Base 5

(106, 138, 504)-Net over F₅ — Constructive and digital

Digital (106, 138, 504)-net over F₅, using

t-expansion [i] based on digital (105, 138, 504)-net over F₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (36, 52, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 26, 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 (53, 86, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 43, 126)-net over F₂₅, using
      - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(106, 138, 4029)-Net over F₅ — Digital

Digital (106, 138, 4029)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 138, 1815901)-Net in Base 5 — Upper bound on s

There is no (106, 138, 1815902)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2 869873 699846 577114 292253 643767 789305 467475 531875 320860 059369 610222 305740 496913 454399 641285 641985 > 5¹³⁸ [i]