MinT - Best Known (40−31, 40, s)-Nets in Base 5

Best Known (40−31, 40, s)-Nets in Base 5

(40−31, 40, 26)-Net over F₅ — Constructive and digital

Digital (9, 40, 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]

(40−31, 40, 84)-Net in Base 5 — Upper bound on s

There is no (9, 40, 85)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁴⁰, 85, S₅, 31), but
- the linear programming bound shows that MÂ â‰¥ 2 520524 123620 197349 216655 886015 484861 010844 279434 679796 133272 298525 889709 708280 861377 716064 453125 / 256 065038 974465 784115 485081 335611 097929 606354 313983 586173 017908 621007 > 5⁴⁰ [i]