MinT - Best Known (28, 28+92, s)-Nets in Base 5

Best Known (28, 28+92, s)-Nets in Base 5

(28, 28+92, 51)-Net over F₅ — Constructive and digital

Digital (28, 120, 51)-net over F₅, using

t-expansion [i] based on digital (22, 120, 51)-net over F₅, using
- net from sequence [i] based on digital (22, 50)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
    - an explicitly constructive algebraic function field [i]

(28, 28+92, 55)-Net over F₅ — Digital

Digital (28, 120, 55)-net over F₅, using

t-expansion [i] based on digital (23, 120, 55)-net over F₅, using
- net from sequence [i] based on digital (23, 54)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 23 and N(F) ≥ 55, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(28, 28+92, 148)-Net in Base 5 — Upper bound on s

There is no (28, 120, 149)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹²⁰, 149, S₅, 92), but
- the linear programming bound shows that MÂ â‰¥ 1875 115433 709844 937609 244603 657370 223629 726878 856922 329955 321895 357533 978909 714278 415776 789188 385009 765625 / 2299 458852 249280 370649 > 5¹²⁰ [i]