MinT - Best Known (38, 38+67, s)-Nets in Base 5

Best Known (38, 38+67, s)-Nets in Base 5

(38, 38+67, 78)-Net over F₅ — Constructive and digital

Digital (38, 105, 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, 38+67, 501)-Net in Base 5 — Upper bound on s

There is no (38, 105, 502)-net in base 5, because

1 times m-reduction [i] would yield (38, 104, 502)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 223702 055182 379226 197577 198667 613608 060931 886063 970411 133355 073603 313625 > 5¹⁰⁴ [i]