MinT - Best Known (36−29, 36, s)-Nets in Base 5

Best Known (36−29, 36, s)-Nets in Base 5

(36−29, 36, 22)-Net over F₅ — Constructive and digital

Digital (7, 36, 22)-net over F₅, using

net from sequence [i] based on digital (7, 21)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 7 and N(F) ≥ 22, using
  - an explicitly constructive algebraic function field [i]

(36−29, 36, 50)-Net in Base 5 — Upper bound on s

There is no (7, 36, 51)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5³⁶, 51, S₅, 29), but
- the linear programming bound shows that MÂ â‰¥ 33434 143915 656022 727489 471435 546875 / 2262 304863 > 5³⁶ [i]