MinT - Best Known (24, 24+76, s)-Nets in Base 5

Best Known (24, 24+76, s)-Nets in Base 5

(24, 24+76, 51)-Net over F₅ — Constructive and digital

Digital (24, 100, 51)-net over F₅, using

t-expansion [i] based on digital (22, 100, 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]

(24, 24+76, 55)-Net over F₅ — Digital

Digital (24, 100, 55)-net over F₅, using

t-expansion [i] based on digital (23, 100, 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]

(24, 24+76, 142)-Net in Base 5 — Upper bound on s

There is no (24, 100, 143)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹⁰⁰, 143, S₅, 76), but
- the linear programming bound shows that MÂ â‰¥ 693930 072990 163203 962309 552355 118881 534525 991176 593876 826229 259735 674990 156191 997703 327700 719455 606304 109096 527099 609375 / 85 477411 271029 008541 378203 422316 524186 769793 755039 > 5¹⁰⁰ [i]