MinT - Best Known (87, 87+63, s)-Nets in Base 5

Best Known (87, 87+63, s)-Nets in Base 5

(87, 87+63, 252)-Net over F₅ — Constructive and digital

Digital (87, 150, 252)-net over F₅, using

t-expansion [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, 87+63, 268)-Net over F₅ — Digital

Digital (87, 150, 268)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(87, 87+63, 7081)-Net in Base 5 — Upper bound on s

There is no (87, 150, 7082)-net in base 5, because

1 times m-reduction [i] would yield (87, 149, 7082)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 140 217247 281870 685514 326209 487073 404859 592483 803880 715890 637069 355480 369425 589167 598327 568247 848236 841417 > 5¹⁴⁹ [i]