Best Known (141, ∞, s)-Nets in Base 3
(141, ∞, 78)-Net over F3 — Constructive and digital
Digital (141, m, 78)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (141, 77)-sequence over F3, using
- t-expansion [i] based on digital (121, 77)-sequence over F3, using
- base reduction for sequences [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- base reduction for sequences [i] based on digital (22, 77)-sequence over F9, using
- t-expansion [i] based on digital (121, 77)-sequence over F3, using
(141, ∞, 120)-Net over F3 — Digital
Digital (141, m, 120)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (141, 119)-sequence over F3, using
- t-expansion [i] based on digital (113, 119)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 113 and N(F) ≥ 120, using
- t-expansion [i] based on digital (113, 119)-sequence over F3, using
(141, ∞, 295)-Net in Base 3 — Upper bound on s
There is no (141, m, 296)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (141, 1769, 296)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31769, 296, S3, 6, 1628), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 063262 461276 457556 536647 179090 640876 983065 445473 860857 052915 371075 338990 030694 757486 293699 883250 607311 350080 191258 986762 491453 613754 424417 848534 004631 337571 215701 414918 772469 215719 782723 640779 875534 122372 960429 273556 156395 089391 660329 674825 470119 789383 208647 098792 481065 868031 159618 746585 640983 205777 172690 893283 304197 270344 693501 863995 695203 273939 917332 395173 250306 551313 091066 133124 307194 126143 862871 467590 790016 984967 054618 432864 555014 707540 829270 405019 977880 698250 664561 645018 758932 513227 107951 806553 151373 777865 685385 690766 557402 218744 052105 415044 575342 119779 220891 024969 196928 442099 830869 873308 375506 466118 397102 351054 740242 217718 524923 597494 575708 935910 060095 033563 096371 493747 983802 646781 796928 192579 805372 810999 639999 918797 167011 027215 736071 026775 882801 518690 104534 501674 553314 955797 155544 141816 370622 658393 237412 721254 411193 922626 887141 / 181 > 31769 [i]
- extracting embedded OOA [i] would yield OOA(31769, 296, S3, 6, 1628), but