MinT - Best Known (45, 45+43, s)-Nets in Base 5

Best Known (45, 45+43, s)-Nets in Base 5

(45, 45+43, 78)-Net over F₅ — Constructive and digital

Digital (45, 88, 78)-net over F₅, using

t-expansion [i] based on digital (38, 88, 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]

(45, 45+43, 102)-Net over F₅ — Digital

Digital (45, 88, 102)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(45, 45+43, 1691)-Net in Base 5 — Upper bound on s

There is no (45, 88, 1692)-net in base 5, because

1 times m-reduction [i] would yield (45, 87, 1692)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6 499708 352600 019584 257956 713873 613740 775936 880602 061522 553585 > 5⁸⁷ [i]