MinT - Best Known (124−28, 124, s)-Nets in Base 5

Best Known (124−28, 124, s)-Nets in Base 5

(124−28, 124, 504)-Net over F₅ — Constructive and digital

Digital (96, 124, 504)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (34, 48, 252)-net over F₅, using
  - trace code for nets [i] based on digital (10, 24, 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 (48, 76, 252)-net over F₅, using
  - trace code for nets [i] based on digital (10, 38, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(124−28, 124, 4444)-Net over F₅ — Digital

Digital (96, 124, 4444)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(124−28, 124, 2345703)-Net in Base 5 — Upper bound on s

There is no (96, 124, 2345704)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 470 199718 382603 589058 943554 511658 315914 024214 665295 127892 261620 735354 831064 830733 149825 > 5¹²⁴ [i]