MinT - Best Known (86, 86+50, s)-Nets in Base 5

Best Known (86, 86+50, s)-Nets in Base 5

(86, 86+50, 252)-Net over F₅ — Constructive and digital

Digital (86, 136, 252)-net over F₅, using

t-expansion [i] based on digital (85, 136, 252)-net over F₅, using
- 14 times m-reduction [i] based on digital (85, 150, 252)-net over F₅, using
  - trace code for nets [i] based on digital (10, 75, 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]

(86, 86+50, 405)-Net over F₅ — Digital

Digital (86, 136, 405)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+50, 16123)-Net in Base 5 — Upper bound on s

There is no (86, 136, 16124)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 114802 367516 324603 981091 379253 729204 729934 344402 627011 103547 338217 017467 002426 850959 809424 496881 > 5¹³⁶ [i]