MinT - Best Known (40, 40+61, s)-Nets in Base 5

Best Known (40, 40+61, s)-Nets in Base 5

(40, 40+61, 78)-Net over F₅ — Constructive and digital

Digital (40, 101, 78)-net over F₅, using

t-expansion [i] based on digital (38, 101, 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]

(40, 40+61, 621)-Net in Base 5 — Upper bound on s

There is no (40, 101, 622)-net in base 5, because

1 times m-reduction [i] would yield (40, 100, 622)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7931 498675 487392 982413 604246 382973 898811 068109 578696 039360 445439 337281 > 5¹⁰⁰ [i]