MinT - Best Known (46−29, 46, s)-Nets in Base 5

Best Known (46−29, 46, s)-Nets in Base 5

(46−29, 46, 42)-Net over F₅ — Constructive and digital

Digital (17, 46, 42)-net over F₅, using

net from sequence [i] based on digital (17, 41)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 17 and N(F) ≥ 42, using
  - an explicitly constructive algebraic function field [i]

(46−29, 46, 256)-Net in Base 5 — Upper bound on s

There is no (17, 46, 257)-net in base 5, because

1 times m-reduction [i] would yield (17, 45, 257)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 28 610230 459502 248256 865010 139625 > 5⁴⁵ [i]