Best Known (36, 36+∞, s)-Nets in Base 5
(36, 36+∞, 72)-Net over F5 — Constructive and digital
Digital (36, m, 72)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (36, 71)-sequence over F5, using
- t-expansion [i] based on digital (31, 71)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 31 and N(F) ≥ 72, using
- t-expansion [i] based on digital (31, 71)-sequence over F5, using
(36, 36+∞, 76)-Net over F5 — Digital
Digital (36, m, 76)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (36, 75)-sequence over F5, using
- t-expansion [i] based on digital (34, 75)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 34 and N(F) ≥ 76, using
- t-expansion [i] based on digital (34, 75)-sequence over F5, using
(36, 36+∞, 160)-Net in Base 5 — Upper bound on s
There is no (36, m, 161)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (36, 479, 161)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5479, 161, S5, 3, 443), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 9 289665 561649 588289 353275 398233 250940 205681 027485 267211 364839 285761 764980 866877 308100 029691 265804 310355 575248 321419 521294 778263 080148 584116 762062 127033 390863 408536 820958 302066 645562 249787 885447 002055 377039 652312 071483 816758 023240 860259 780002 668764 832423 726876 758222 936249 358713 444838 053952 481060 800139 278654 796726 186759 769916 534423 828125 / 111 > 5479 [i]
- extracting embedded OOA [i] would yield OOA(5479, 161, S5, 3, 443), but