Best Known (5, ∞, s)-Nets in Base 27
(5, ∞, 68)-Net over F27 — Constructive and digital
Digital (5, m, 68)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
(5, ∞, 72)-Net over F27 — Digital
Digital (5, m, 72)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (5, 71)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 72, using
(5, ∞, 168)-Net in Base 27 — Upper bound on s
There is no (5, m, 169)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (5, 167, 169)-net in base 27, but
- extracting embedded OOA [i] would yield OA(27167, 169, S27, 162), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 20 616285 448258 254189 632446 434101 061939 919259 309742 920263 876202 317073 200308 628068 739540 554185 109313 440135 737891 337006 986211 869313 170146 408503 076708 329690 668617 272344 297529 613836 221069 388332 816090 054458 740691 616512 138780 754856 409263 979104 870567 / 163 > 27167 [i]
- extracting embedded OOA [i] would yield OA(27167, 169, S27, 162), but