MinT - Best Known (86, 86+59, s)-Nets in Base 5

Best Known (86, 86+59, s)-Nets in Base 5

(86, 86+59, 252)-Net over F₅ — Constructive and digital

Digital (86, 145, 252)-net over F₅, using

t-expansion [i] based on digital (85, 145, 252)-net over F₅, using
- 5 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+59, 292)-Net over F₅ — Digital

Digital (86, 145, 292)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+59, 8604)-Net in Base 5 — Upper bound on s

There is no (86, 145, 8605)-net in base 5, because

1 times m-reduction [i] would yield (86, 144, 8605)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 44875 854971 127089 633296 402529 652682 906338 435298 578445 756942 271134 090423 256226 104025 899398 451467 018181 > 5¹⁴⁴ [i]