MinT - Best Known (86−23, 86, s)-Nets in Base 5

Best Known (86−23, 86, s)-Nets in Base 5

(86−23, 86, 296)-Net over F₅ — Constructive and digital

Digital (63, 86, 296)-net over F₅, using

2 times m-reduction [i] based on digital (63, 88, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 44, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(86−23, 86, 1233)-Net over F₅ — Digital

Digital (63, 86, 1233)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(86−23, 86, 309083)-Net in Base 5 — Upper bound on s

There is no (63, 86, 309084)-net in base 5, because

1 times m-reduction [i] would yield (63, 85, 309084)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 258503 086606 482807 900632 859284 994171 950803 682030 440739 134065 > 5⁸⁵ [i]