MinT - Best Known (30−19, 30, s)-Nets in Base 5

Best Known (30−19, 30, s)-Nets in Base 5

(30−19, 30, 32)-Net over F₅ — Constructive and digital

Digital (11, 30, 32)-net over F₅, using

net from sequence [i] based on digital (11, 31)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 11 and N(F) ≥ 32, using
  - an explicitly constructive algebraic function field [i]

(30−19, 30, 179)-Net in Base 5 — Upper bound on s

There is no (11, 30, 180)-net in base 5, because

1 times m-reduction [i] would yield (11, 29, 180)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 194 098614 632259 648465 > 5²⁹ [i]