MinT - Best Known (41−32, 41, s)-Nets in Base 5

Best Known (41−32, 41, s)-Nets in Base 5

(41−32, 41, 26)-Net over F₅ — Constructive and digital

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]

(41−32, 41, 79)-Net in Base 5 — Upper bound on s

There is no (9, 41, 80)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁴¹, 80, S₅, 32), but
- the linear programming bound shows that MÂ â‰¥ 13 252773 306666 657353 593860 851023 862021 344802 402131 867584 043210 660594 888861 623985 576443 374156 951904 296875 / 272 656715 111265 530912 564214 275116 750816 999102 387552 399161 770641 760349 218051 > 5⁴¹ [i]