MinT - Best Known (93−55, 93, s)-Nets in Base 5

Best Known (93−55, 93, s)-Nets in Base 5

(93−55, 93, 78)-Net over F₅ — Constructive and digital

Digital (38, 93, 78)-net over F₅, using

net from sequence [i] based on digital (38, 77)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
  - an explicitly constructive algebraic function field [i]

(93−55, 93, 638)-Net in Base 5 — Upper bound on s

There is no (38, 93, 639)-net in base 5, because

1 times m-reduction [i] would yield (38, 92, 639)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 20910 449877 412333 232637 597762 163841 639297 036325 495930 604339 179925 > 5⁹² [i]