MinT - Best Known (129−91, 129, s)-Nets in Base 5

Best Known (129−91, 129, s)-Nets in Base 5

(129−91, 129, 78)-Net over F₅ — Constructive and digital

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]

(129−91, 129, 396)-Net in Base 5 — Upper bound on s

There is no (38, 129, 397)-net in base 5, because

1 times m-reduction [i] would yield (38, 128, 397)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 310573 895384 855466 712180 178814 795359 699530 494634 923176 206836 363900 044863 701895 446757 167685 > 5¹²⁸ [i]