MinT - Best Known (41−26, 41, s)-Nets in Base 3

Best Known (41−26, 41, s)-Nets in Base 3

(41−26, 41, 28)-Net over F₃ — Constructive and digital

Digital (15, 41, 28)-net over F₃, using

net from sequence [i] based on digital (15, 27)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
  - an explicitly constructive algebraic function field [i]

(41−26, 41, 77)-Net in Base 3 — Upper bound on s

There is no (15, 41, 78)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁴¹, 78, S₃, 26), but
- the linear programming bound shows that MÂ â‰¥ 56 086862 089601 057123 877652 162404 701632 497035 243812 015612 219423 457555 825513 955696 341979 689727 927642 785758 924509 / 1 503427 202045 128664 660261 886336 874448 650564 537886 648817 115912 785764 682742 046514 235503 869650 > 3⁴¹ [i]