MinT - Best Known (124−45, 124, s)-Nets in Base 5

Best Known (124−45, 124, s)-Nets in Base 5

(124−45, 124, 252)-Net over F₅ — Constructive and digital

Digital (79, 124, 252)-net over F₅, using

14 times m-reduction [i] based on digital (79, 138, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 69, 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]

(124−45, 124, 396)-Net over F₅ — Digital

Digital (79, 124, 396)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(124−45, 124, 18293)-Net in Base 5 — Upper bound on s

There is no (79, 124, 18294)-net in base 5, because

1 times m-reduction [i] would yield (79, 123, 18294)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 94 122653 379191 649077 338933 660521 606750 317180 250894 691762 416678 841458 945321 453677 931585 > 5¹²³ [i]