MinT - Best Known (9, 9+19, s)-Nets in Base 5

Best Known (9, 9+19, s)-Nets in Base 5

(9, 9+19, 26)-Net over F₅ — Constructive and digital

Digital (9, 28, 26)-net over F₅, using

net from sequence [i] based on digital (9, 25)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 9 and N(F) ≥ 26, using
  - an explicitly constructive algebraic function field [i]

(9, 9+19, 123)-Net in Base 5 — Upper bound on s

There is no (9, 28, 124)-net in base 5, because

1 times m-reduction [i] would yield (9, 27, 124)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7 735343 304202 164465 > 5²⁷ [i]