Best Known (129−74, 129, s)-Nets in Base 3
(129−74, 129, 48)-Net over F3 — Constructive and digital
Digital (55, 129, 48)-net over F3, using
- t-expansion [i] based on digital (45, 129, 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
(129−74, 129, 64)-Net over F3 — Digital
Digital (55, 129, 64)-net over F3, using
- t-expansion [i] based on digital (49, 129, 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
(129−74, 129, 297)-Net in Base 3 — Upper bound on s
There is no (55, 129, 298)-net in base 3, because
- 1 times m-reduction [i] would yield (55, 128, 298)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3128, 298, S3, 73), but
- 2 times code embedding in larger space [i] would yield OA(3130, 300, S3, 73), but
- the linear programming bound shows that M ≥ 34 610846 936085 940449 136399 594888 261707 076098 331375 234200 879736 710721 930828 733231 427259 935444 082850 600309 566608 839070 572720 620045 675692 211479 018680 688476 354313 446910 843929 372556 483793 644243 531958 816256 587387 727430 629636 272163 080005 807201 401339 534943 886440 508056 510765 690232 650865 747684 448037 551496 533505 004956 600886 618725 540166 116713 472588 851479 066992 886836 337516 626036 450236 180159 879582 220179 842509 104033 812274 042568 981875 957701 498969 315987 806875 491444 585758 766567 689440 660855 703268 925380 168934 458191 197724 247073 258123 480918 843710 441067 078350 143622 857085 922730 938913 860538 517432 797109 688354 394542 599742 235702 872198 662096 482373 891764 452301 228532 675805 357784 765692 089857 374760 676538 620368 806632 237924 147783 833796 726175 123661 893428 099253 847388 030137 253920 403849 776012 022395 148007 444687 022763 160840 971511 126245 002705 221999 819463 194342 125596 853846 357213 064861 250120 690698 862780 159270 947554 927153 464772 574524 311207 956428 828125 / 316900 634457 582877 476428 992569 632177 851222 751957 161544 418860 901461 691355 484290 188016 617176 188312 085781 493021 945309 019071 070423 133074 605039 790619 762216 591260 590945 672283 099677 229410 039691 961776 586704 811354 608888 720037 941688 043624 502184 424031 496983 401398 967081 698124 718355 526719 226734 219205 642105 943587 647189 715175 045133 172089 344352 447442 919095 963038 933215 297516 006757 392477 031244 672067 060890 106377 872989 008786 593220 633630 779440 475336 357803 237836 791997 058240 698994 939590 719475 401919 592275 736666 492848 756193 379497 156808 417594 906100 182216 963015 285692 743225 955798 291109 606670 061342 911886 220893 412539 013323 698131 424837 632500 525833 287917 175288 215514 509526 807694 732838 273910 474757 370864 339092 739630 992058 361671 691413 628364 429997 144804 034640 043801 337519 042158 094623 368691 510951 831690 724136 537106 529795 810164 194542 151377 438694 556299 619648 301162 781394 578946 609538 013229 > 3130 [i]
- 2 times code embedding in larger space [i] would yield OA(3130, 300, S3, 73), but
- extracting embedded orthogonal array [i] would yield OA(3128, 298, S3, 73), but