MinT - Best Known (104−81, 104, s)-Nets in Base 5

Best Known (104−81, 104, s)-Nets in Base 5

(104−81, 104, 51)-Net over F₅ — Constructive and digital

Digital (23, 104, 51)-net over F₅, using

t-expansion [i] based on digital (22, 104, 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]

(104−81, 104, 55)-Net over F₅ — Digital

Digital (23, 104, 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]

(104−81, 104, 121)-Net in Base 5 — Upper bound on s

There is no (23, 104, 122)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹⁰⁴, 122, S₅, 81), but
- the linear programming bound shows that MÂ â‰¥ 26 765091 755407 735481 416525 305329 470914 633888 979639 042560 165762 552060 186862 945556 640625 / 4 517751 405839 > 5¹⁰⁴ [i]