MinT - Best Known (75−53, 75, s)-Nets in Base 5

Best Known (75−53, 75, s)-Nets in Base 5

(75−53, 75, 51)-Net over F₅ — Constructive and digital

Digital (22, 75, 51)-net over F₅, using

net from sequence [i] based on digital (22, 50)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
  - an explicitly constructive algebraic function field [i]

(75−53, 75, 238)-Net in Base 5 — Upper bound on s

There is no (22, 75, 239)-net in base 5, because

1 times m-reduction [i] would yield (22, 74, 239)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5354 835102 794150 505267 368319 039217 671803 503942 138777 > 5⁷⁴ [i]