Best Known (18, 18+30, s)-Nets in Base 3
(18, 18+30, 28)-Net over F3 — Constructive and digital
Digital (18, 48, 28)-net over F3, using
- t-expansion [i] based on digital (15, 48, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 15 and N(F) ≥ 28, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
(18, 18+30, 91)-Net in Base 3 — Upper bound on s
There is no (18, 48, 92)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(348, 92, S3, 30), but
- the linear programming bound shows that M ≥ 155 048411 553818 226984 162442 805466 373690 213914 286977 371705 202589 167499 618075 777887 490030 565740 317397 764959 550584 283305 143182 198684 333887 858697 429357 / 1910 711961 142437 205632 506964 219549 741634 425447 199116 992722 054136 110889 532920 784510 794697 061627 361802 892124 313524 414123 148275 > 348 [i]