Best Known (59−35, 59, s)-Nets in Base 3
(59−35, 59, 32)-Net over F3 — Constructive and digital
Digital (24, 59, 32)-net over F3, using
- t-expansion [i] based on digital (21, 59, 32)-net over F3, using
- net from sequence [i] based on digital (21, 31)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 21 and N(F) ≥ 32, using
- net from sequence [i] based on digital (21, 31)-sequence over F3, using
(59−35, 59, 135)-Net in Base 3 — Upper bound on s
There is no (24, 59, 136)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(359, 136, S3, 35), but
- the linear programming bound shows that M ≥ 22 726839 204691 891253 644696 898369 207187 081234 181735 714843 341275 897616 762362 710018 187521 018627 172327 868695 031408 531569 772970 640083 192156 200366 308595 435159 925930 757650 433436 609239 366400 / 1549 254697 196676 010642 793897 637084 831954 187799 248006 962271 072379 219020 389873 109263 689496 974500 056880 902187 125508 048087 135151 525741 030050 717474 931926 817179 > 359 [i]