MinT - Best Known (125−101, 125, s)-Nets in Base 5

Best Known (125−101, 125, s)-Nets in Base 5

(125−101, 125, 51)-Net over F₅ — Constructive and digital

Digital (24, 125, 51)-net over F₅, using

t-expansion [i] based on digital (22, 125, 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]

(125−101, 125, 55)-Net over F₅ — Digital

Digital (24, 125, 55)-net over F₅, using

t-expansion [i] based on digital (23, 125, 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]

(125−101, 125, 124)-Net in Base 5 — Upper bound on s

There is no (24, 125, 125)-net in base 5, because

13 times m-reduction [i] would yield (24, 112, 125)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(5¹¹², 125, S₅, 88), but
  - the linear programming bound shows that MÂ â‰¥ 34583 984196 672356 314446 603914 308245 637967 395612 680232 552804 682200 076058 506965 637207 031250 / 13859 944813 > 5¹¹² [i]