MinT - Best Known (10, 10+39, s)-Nets in Base 5

Best Known (10, 10+39, s)-Nets in Base 5

(10, 10+39, 26)-Net over F₅ — Constructive and digital

Digital (10, 49, 26)-net over F₅, using

t-expansion [i] based on digital (9, 49, 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+39, 27)-Net over F₅ — Digital

Digital (10, 49, 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+39, 64)-Net in Base 5 — Upper bound on s

There is no (10, 49, 65)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁴⁹, 65, S₅, 39), but
- the linear programming bound shows that MÂ â‰¥ 166 547764 468560 899331 350810 825824 737548 828125 / 7743 671901 > 5⁴⁹ [i]