MinT - Best Known (140−88, 140, s)-Nets in Base 5

Best Known (140−88, 140, s)-Nets in Base 5

(140−88, 140, 82)-Net over F₅ — Constructive and digital

Digital (52, 140, 82)-net over F₅, using

t-expansion [i] based on digital (48, 140, 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]

(140−88, 140, 104)-Net over F₅ — Digital

Digital (52, 140, 104)-net over F₅, using

t-expansion [i] based on digital (51, 140, 104)-net over F₅, using
- net from sequence [i] based on digital (51, 103)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 51 and N(F) ≥ 104, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(140−88, 140, 690)-Net in Base 5 — Upper bound on s

There is no (52, 140, 691)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 73 771281 503325 843988 146874 179946 710400 793870 247621 961537 914729 256298 400335 712854 314497 988565 929425 > 5¹⁴⁰ [i]