MinT - Best Known (86, 86+48, s)-Nets in Base 5

Best Known (86, 86+48, s)-Nets in Base 5

(86, 86+48, 296)-Net over F₅ — Constructive and digital

Digital (86, 134, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 67, 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, 86+48, 445)-Net over F₅ — Digital

Digital (86, 134, 445)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+48, 19565)-Net in Base 5 — Upper bound on s

There is no (86, 134, 19566)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4593 023037 680150 665319 294535 428236 120841 431064 365316 504107 609285 595480 963466 635639 186758 455425 > 5¹³⁴ [i]