MinT - Best Known (87, 87+57, s)-Nets in Base 5

Best Known (87, 87+57, s)-Nets in Base 5

(87, 87+57, 252)-Net over F₅ — Constructive and digital

Digital (87, 144, 252)-net over F₅, using

t-expansion [i] based on digital (85, 144, 252)-net over F₅, using
- 6 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, 87+57, 321)-Net over F₅ — Digital

Digital (87, 144, 321)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(87, 87+57, 10467)-Net in Base 5 — Upper bound on s

There is no (87, 144, 10468)-net in base 5, because

1 times m-reduction [i] would yield (87, 143, 10468)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 8984 563828 559253 403962 721405 837736 402275 580512 139223 530730 454748 477274 781273 164963 014314 549760 281345 > 5¹⁴³ [i]