MinT - Best Known (99−61, 99, s)-Nets in Base 5

Best Known (99−61, 99, s)-Nets in Base 5

(99−61, 99, 78)-Net over F₅ — Constructive and digital

Digital (38, 99, 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]

(99−61, 99, 556)-Net in Base 5 — Upper bound on s

There is no (38, 99, 557)-net in base 5, because

1 times m-reduction [i] would yield (38, 98, 557)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 324 994633 983511 156637 919087 197579 194510 774476 376694 060348 032732 779817 > 5⁹⁸ [i]