MinT - Best Known (87, 87+59, s)-Nets in Base 5

Best Known (87, 87+59, s)-Nets in Base 5

(87, 87+59, 252)-Net over F₅ — Constructive and digital

Digital (87, 146, 252)-net over F₅, using

t-expansion [i] based on digital (85, 146, 252)-net over F₅, using
- 4 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+59, 301)-Net over F₅ — Digital

Digital (87, 146, 301)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(87, 87+59, 9097)-Net in Base 5 — Upper bound on s

There is no (87, 146, 9098)-net in base 5, because

1 times m-reduction [i] would yield (87, 145, 9098)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 224900 786745 558829 961834 178972 015798 114581 241908 720212 546724 877909 352027 427646 074224 239087 928011 793705 > 5¹⁴⁵ [i]