MinT - Best Known (86−64, 86, s)-Nets in Base 5

Best Known (86−64, 86, s)-Nets in Base 5

(86−64, 86, 51)-Net over F₅ — Constructive and digital

Digital (22, 86, 51)-net over F₅, using

net from sequence [i] based on digital (22, 50)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
  - an explicitly constructive algebraic function field [i]

(86−64, 86, 218)-Net in Base 5 — Upper bound on s

There is no (22, 86, 219)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 293279 568690 516890 727865 198068 677245 621366 266143 465880 402817 > 5⁸⁶ [i]