MinT - Best Known (99−47, 99, s)-Nets in Base 5

Best Known (99−47, 99, s)-Nets in Base 5

(99−47, 99, 82)-Net over F₅ — Constructive and digital

Digital (52, 99, 82)-net over F₅, using

t-expansion [i] based on digital (48, 99, 82)-net over F₅, using
- net from sequence [i] based on digital (48, 81)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 48 and N(F) ≥ 82, using
    - an explicitly constructive algebraic function field [i]

(99−47, 99, 123)-Net over F₅ — Digital

Digital (52, 99, 123)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−47, 99, 2225)-Net in Base 5 — Upper bound on s

There is no (52, 99, 2226)-net in base 5, because

1 times m-reduction [i] would yield (52, 98, 2226)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 318 159798 160093 078681 241599 037230 040994 690911 935503 152527 911776 072425 > 5⁹⁸ [i]