MinT - Best Known (87, 142, s)-Nets in Base 5

Best Known (87, 142, s)-Nets in Base 5

(87, 142, 252)-Net over F₅ — Constructive and digital

Digital (87, 142, 252)-net over F₅, using

t-expansion [i] based on digital (85, 142, 252)-net over F₅, using
- 8 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]

(87, 142, 343)-Net over F₅ — Digital

Digital (87, 142, 343)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(87, 142, 12184)-Net in Base 5 — Upper bound on s

There is no (87, 142, 12185)-net in base 5, because

1 times m-reduction [i] would yield (87, 141, 12185)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 358 844201 192849 979355 957158 294413 029985 011433 788913 161997 978778 598453 743512 270937 458063 243233 105533 > 5¹⁴¹ [i]