MinT - Best Known (38, 115, s)-Nets in Base 5

Best Known (38, 115, s)-Nets in Base 5

(38, 115, 78)-Net over F₅ — Constructive and digital

Digital (38, 115, 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]

(38, 115, 442)-Net in Base 5 — Upper bound on s

There is no (38, 115, 443)-net in base 5, because

1 times m-reduction [i] would yield (38, 114, 443)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 51 795675 175495 395090 540895 189647 887605 998460 624584 489044 135222 766957 520918 160745 > 5¹¹⁴ [i]