MinT - Best Known (129−89, 129, s)-Nets in Base 5

Best Known (129−89, 129, s)-Nets in Base 5

(129−89, 129, 78)-Net over F₅ — Constructive and digital

Digital (40, 129, 78)-net over F₅, using

t-expansion [i] based on digital (38, 129, 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]

(129−89, 129, 434)-Net in Base 5 — Upper bound on s

There is no (40, 129, 435)-net in base 5, because

1 times m-reduction [i] would yield (40, 128, 435)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 319556 651951 601414 505541 864498 121671 910198 743459 742533 893071 163532 137616 482924 435852 570065 > 5¹²⁸ [i]