Best Known (161−102, 161, s)-Nets in Base 3
(161−102, 161, 48)-Net over F3 — Constructive and digital
Digital (59, 161, 48)-net over F3, using
- t-expansion [i] based on digital (45, 161, 48)-net over F3, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
(161−102, 161, 64)-Net over F3 — Digital
Digital (59, 161, 64)-net over F3, using
- t-expansion [i] based on digital (49, 161, 64)-net over F3, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 49 and N(F) ≥ 64, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
(161−102, 161, 251)-Net over F3 — Upper bound on s (digital)
There is no digital (59, 161, 252)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(3161, 252, F3, 102) (dual of [252, 91, 103]-code), but
- residual code [i] would yield OA(359, 149, S3, 34), but
- the linear programming bound shows that M ≥ 161072 631961 680185 280440 930117 244701 258542 024979 482340 755321 093357 664942 075114 897456 280621 705350 294957 376375 / 10 335291 754987 667559 057108 370888 319896 679664 836625 228437 457068 286900 284102 491501 > 359 [i]
- residual code [i] would yield OA(359, 149, S3, 34), but
(161−102, 161, 271)-Net in Base 3 — Upper bound on s
There is no (59, 161, 272)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 76779 258884 151635 322369 779942 340145 035595 311122 601558 772074 717361 273386 787905 > 3161 [i]