MinT - Best Known (87−49, 87, s)-Nets in Base 5

Best Known (87−49, 87, s)-Nets in Base 5

(87−49, 87, 78)-Net over F₅ — Constructive and digital

Digital (38, 87, 78)-net over F₅, using

net from sequence [i] based on digital (38, 77)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
  - an explicitly constructive algebraic function field [i]

(87−49, 87, 765)-Net in Base 5 — Upper bound on s

There is no (38, 87, 766)-net in base 5, because

1 times m-reduction [i] would yield (38, 86, 766)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 293655 250330 916382 786865 124273 290161 699334 736657 917093 482625 > 5⁸⁶ [i]