MinT - Best Known (79, 137, s)-Nets in Base 5

Best Known (79, 137, s)-Nets in Base 5

(79, 137, 252)-Net over F₅ — Constructive and digital

Digital (79, 137, 252)-net over F₅, using

1 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]

(79, 137, 5827)-Net in Base 5 — Upper bound on s

There is no (79, 137, 5828)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 574178 300076 852409 539254 369588 500099 747212 432279 561779 798553 706309 066150 893731 016360 642007 348625 > 5¹³⁷ [i]