MinT - Best Known (10, 41, s)-Nets in Base 5

Best Known (10, 41, s)-Nets in Base 5

(10, 41, 26)-Net over F₅ — Constructive and digital

Digital (10, 41, 26)-net over F₅, using

t-expansion [i] based on digital (9, 41, 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, 41, 27)-Net over F₅ — Digital

Digital (10, 41, 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, 41, 101)-Net in Base 5 — Upper bound on s

There is no (10, 41, 102)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁴¹, 102, S₅, 31), but
- the linear programming bound shows that MÂ â‰¥ 55 197468 656583 420453 542280 232262 713301 968982 332729 292102 158069 610595 703125 / 1191 665448 042021 284819 913432 191826 628668 422893 > 5⁴¹ [i]