MinT - Best Known (112−73, 112, s)-Nets in Base 5

Best Known (112−73, 112, s)-Nets in Base 5

(112−73, 112, 78)-Net over F₅ — Constructive and digital

Digital (39, 112, 78)-net over F₅, using

t-expansion [i] based on digital (38, 112, 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]

(112−73, 112, 484)-Net in Base 5 — Upper bound on s

There is no (39, 112, 485)-net in base 5, because

1 times m-reduction [i] would yield (39, 111, 485)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 404977 862860 029357 475748 493243 841000 967887 118247 969832 028672 756239 713163 576945 > 5¹¹¹ [i]