MinT - Best Known (67−33, 67, s)-Nets in Base 5

Best Known (67−33, 67, s)-Nets in Base 5

(67−33, 67, 72)-Net over F₅ — Constructive and digital

Digital (34, 67, 72)-net over F₅, using

t-expansion [i] based on digital (31, 67, 72)-net over F₅, using
- net from sequence [i] based on digital (31, 71)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 31 and N(F) ≥ 72, using
    - an explicitly constructive algebraic function field [i]

(67−33, 67, 80)-Net over F₅ — Digital

Digital (34, 67, 80)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(67−33, 67, 1287)-Net in Base 5 — Upper bound on s

There is no (34, 67, 1288)-net in base 5, because

1 times m-reduction [i] would yield (34, 66, 1288)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 13569 492309 966222 102688 529629 167413 102013 958145 > 5⁶⁶ [i]