MinT - Best Known (146−77, 146, s)-Nets in Base 5

Best Known (146−77, 146, s)-Nets in Base 5

(146−77, 146, 82)-Net over F₅ — Constructive and digital

Digital (69, 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]

(146−77, 146, 132)-Net over F₅ — Digital

Digital (69, 146, 132)-net over F₅, using

t-expansion [i] based on 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]

(146−77, 146, 1717)-Net in Base 5 — Upper bound on s

There is no (69, 146, 1718)-net in base 5, because

1 times m-reduction [i] would yield (69, 145, 1718)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 226953 771608 875264 534304 003122 826856 098617 411742 887355 978903 422418 888801 926930 118062 287642 361673 002305 > 5¹⁴⁵ [i]