MinT - Best Known (10, 10+38, s)-Nets in Base 5

Best Known (10, 10+38, s)-Nets in Base 5

(10, 10+38, 26)-Net over F₅ — Constructive and digital

Digital (10, 48, 26)-net over F₅, using

t-expansion [i] based on digital (9, 48, 26)-net over F₅, using
- net from sequence [i] based on digital (9, 25)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 9 and N(F) ≥ 26, using
    - an explicitly constructive algebraic function field [i]

(10, 10+38, 27)-Net over F₅ — Digital

Digital (10, 48, 27)-net over F₅, using

net from sequence [i] based on digital (10, 26)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 10 and N(F) ≥ 27, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(10, 10+38, 69)-Net in Base 5 — Upper bound on s

There is no (10, 48, 70)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁴⁸, 70, S₅, 38), but
- the linear programming bound shows that MÂ â‰¥ 539440 562069 576967 640927 023239 783011 376857 757568 359375 / 139 883917 548885 212703 > 5⁴⁸ [i]