MinT - Best Known (139−59, 139, s)-Nets in Base 5

Best Known (139−59, 139, s)-Nets in Base 5

(139−59, 139, 252)-Net over F₅ — Constructive and digital

Digital (80, 139, 252)-net over F₅, using

1 times m-reduction [i] based on digital (80, 140, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 70, 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]

(139−59, 139, 6161)-Net in Base 5 — Upper bound on s

There is no (80, 139, 6162)-net in base 5, because

1 times m-reduction [i] would yield (80, 138, 6162)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2 873657 950186 069125 690746 137429 996427 204207 139120 821612 234390 623335 004862 155681 849323 571355 932745 > 5¹³⁸ [i]