MinT - Best Known (40, 40+77, s)-Nets in Base 5

Best Known (40, 40+77, s)-Nets in Base 5

(40, 40+77, 78)-Net over F₅ — Constructive and digital

Digital (40, 117, 78)-net over F₅, using

t-expansion [i] based on digital (38, 117, 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+77, 483)-Net in Base 5 — Upper bound on s

There is no (40, 117, 484)-net in base 5, because

1 times m-reduction [i] would yield (40, 116, 484)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1244 052786 896566 980511 760218 269597 831783 116495 755955 630733 466204 243307 927745 011905 > 5¹¹⁶ [i]