MinT - Best Known (107−82, 107, s)-Nets in Base 5

Best Known (107−82, 107, s)-Nets in Base 5

(107−82, 107, 51)-Net over F₅ — Constructive and digital

Digital (25, 107, 51)-net over F₅, using

t-expansion [i] based on digital (22, 107, 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]

(107−82, 107, 55)-Net over F₅ — Digital

Digital (25, 107, 55)-net over F₅, using

t-expansion [i] based on digital (23, 107, 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]

(107−82, 107, 135)-Net in Base 5 — Upper bound on s

There is no (25, 107, 136)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹⁰⁷, 136, S₅, 82), but
- the linear programming bound shows that MÂ â‰¥ 4 680614 732900 044285 630127 740921 339805 504137 246651 693367 478774 820966 691549 983806 908130 645751 953125 / 7377 156347 408094 956731 > 5¹⁰⁷ [i]