MinT - Best Known (39, 39+63, s)-Nets in Base 5

Best Known (39, 39+63, s)-Nets in Base 5

(39, 39+63, 78)-Net over F₅ — Constructive and digital

Digital (39, 102, 78)-net over F₅, using

t-expansion [i] based on digital (38, 102, 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]

(39, 39+63, 565)-Net in Base 5 — Upper bound on s

There is no (39, 102, 566)-net in base 5, because

1 times m-reduction [i] would yield (39, 101, 566)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 40703 114037 504365 778950 959975 001885 714862 894646 694800 638016 673524 836345 > 5¹⁰¹ [i]