MinT - Best Known (34, 34+31, s)-Nets in Base 5

Best Known (34, 34+31, s)-Nets in Base 5

(34, 34+31, 72)-Net over F₅ — Constructive and digital

Digital (34, 65, 72)-net over F₅, using

t-expansion [i] based on digital (31, 65, 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]

(34, 34+31, 88)-Net over F₅ — Digital

Digital (34, 65, 88)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(34, 34+31, 1530)-Net in Base 5 — Upper bound on s

There is no (34, 65, 1531)-net in base 5, because

1 times m-reduction [i] would yield (34, 64, 1531)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 542 618359 067932 538079 085597 838452 608241 468405 > 5⁶⁴ [i]