Best Known (41, 41+∞, s)-Nets in Base 5
(41, 41+∞, 78)-Net over F5 — Constructive and digital
Digital (41, m, 78)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (41, 77)-sequence over F5, using
- t-expansion [i] based on digital (38, 77)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 38 and N(F) ≥ 78, using
- t-expansion [i] based on digital (38, 77)-sequence over F5, using
(41, 41+∞, 80)-Net over F5 — Digital
Digital (41, m, 80)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (41, 79)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 41 and N(F) ≥ 80, using
(41, 41+∞, 180)-Net in Base 5 — Upper bound on s
There is no (41, m, 181)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (41, 539, 181)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5539, 181, S5, 3, 498), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 30 840777 649105 450082 767648 623004 021344 661278 290325 595634 584819 338690 374074 234930 122193 523229 451756 409299 663750 879384 847779 900313 115492 783312 274675 670442 037312 478570 191092 220429 404364 982380 506179 723909 777943 867986 610568 244603 474598 017465 965351 214920 148068 277933 390955 399812 380689 209451 741714 268961 360496 441089 120543 123833 459057 603328 997017 831658 578046 472030 109725 892543 792724 609375 / 499 > 5539 [i]
- extracting embedded OOA [i] would yield OOA(5539, 181, S5, 3, 498), but