MinT - Best Known (28−21, 28, s)-Nets in Base 5

Best Known (28−21, 28, s)-Nets in Base 5

(28−21, 28, 22)-Net over F₅ — Constructive and digital

Digital (7, 28, 22)-net over F₅, using

net from sequence [i] based on digital (7, 21)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 7 and N(F) ≥ 22, using
  - an explicitly constructive algebraic function field [i]

(28−21, 28, 80)-Net in Base 5 — Upper bound on s

There is no (7, 28, 81)-net in base 5, because

1 times m-reduction [i] would yield (7, 27, 81)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7 866252 142412 394745 > 5²⁷ [i]