MinT - Best Known (40, 40+67, s)-Nets in Base 5

Best Known (40, 40+67, s)-Nets in Base 5

(40, 40+67, 78)-Net over F₅ — Constructive and digital

Digital (40, 107, 78)-net over F₅, using

t-expansion [i] based on digital (38, 107, 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+67, 554)-Net in Base 5 — Upper bound on s

There is no (40, 107, 555)-net in base 5, because

1 times m-reduction [i] would yield (40, 106, 555)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 124 469501 147237 297249 836860 739279 437436 511010 794339 574769 435036 563105 751085 > 5¹⁰⁶ [i]