MinT - Best Known (67, 146, s)-Nets in Base 5

Best Known (67, 146, s)-Nets in Base 5

(67, 146, 82)-Net over F₅ — Constructive and digital

Digital (67, 146, 82)-net over F₅, using

t-expansion [i] based on digital (48, 146, 82)-net over F₅, using
- net from sequence [i] based on digital (48, 81)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 48 and N(F) ≥ 82, using
    - an explicitly constructive algebraic function field [i]

(67, 146, 132)-Net over F₅ — Digital

Digital (67, 146, 132)-net over F₅, using

net from sequence [i] based on digital (67, 131)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 67 and N(F) ≥ 132, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(67, 146, 1499)-Net in Base 5 — Upper bound on s

There is no (67, 146, 1500)-net in base 5, because

1 times m-reduction [i] would yield (67, 145, 1500)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 227907 850838 907993 955399 884041 727535 711895 106995 593311 588979 360797 872021 709797 621196 210213 886886 720241 > 5¹⁴⁵ [i]