MinT - Best Known (24, 105, s)-Nets in Base 5

Best Known (24, 105, s)-Nets in Base 5

(24, 105, 51)-Net over F₅ — Constructive and digital

Digital (24, 105, 51)-net over F₅, using

t-expansion [i] based on digital (22, 105, 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, 105, 55)-Net over F₅ — Digital

Digital (24, 105, 55)-net over F₅, using

t-expansion [i] based on digital (23, 105, 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, 105, 128)-Net in Base 5 — Upper bound on s

There is no (24, 105, 129)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹⁰⁵, 129, S₅, 81), but
- the linear programming bound shows that MÂ â‰¥ 2 767845 571184 343042 241526 773779 517697 880400 524585 754740 147791 608251 282013 952732 086181 640625 / 91313 204084 993462 > 5¹⁰⁵ [i]