MinT - Best Known (22, 79, s)-Nets in Base 5

Best Known (22, 79, s)-Nets in Base 5

(22, 79, 51)-Net over F₅ — Constructive and digital

Digital (22, 79, 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]

(22, 79, 230)-Net in Base 5 — Upper bound on s

There is no (22, 79, 231)-net in base 5, because

1 times m-reduction [i] would yield (22, 78, 231)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3 635970 171047 954355 596309 824345 228171 170818 026349 330065 > 5⁷⁸ [i]