Best Known (131−75, 131, s)-Nets in Base 3
(131−75, 131, 48)-Net over F3 — Constructive and digital
Digital (56, 131, 48)-net over F3, using
- t-expansion [i] based on digital (45, 131, 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
(131−75, 131, 64)-Net over F3 — Digital
Digital (56, 131, 64)-net over F3, using
- t-expansion [i] based on digital (49, 131, 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
(131−75, 131, 297)-Net in Base 3 — Upper bound on s
There is no (56, 131, 298)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(3131, 298, S3, 75), but
- 2 times code embedding in larger space [i] would yield OA(3133, 300, S3, 75), but
- the linear programming bound shows that M ≥ 106 333117 774812 249541 811383 356915 240363 193027 991729 658667 984018 571479 238017 901410 343412 096880 048002 132667 440560 291353 567384 535635 991451 471154 016078 875645 120696 786257 514604 330080 847391 789957 246976 769260 907677 274333 010040 784557 376068 639499 532489 241952 409296 901914 103512 813170 466444 717117 195885 293632 170796 882652 843866 158846 572878 907745 068593 169898 802303 905156 298605 946805 265265 408202 081114 097618 921035 689735 532651 596780 605044 557174 201333 663606 230896 017947 298666 137463 926099 830454 622613 559856 151226 336978 223262 390925 913403 286489 691593 279489 127243 089955 740506 196924 457643 904769 860950 727491 939754 396595 308730 670944 380922 994453 587027 814300 894619 154033 289123 624466 474517 126780 618458 238860 236901 176005 736268 315794 110834 002252 192859 223904 044858 474690 240897 209613 698473 559236 707743 376110 088064 652859 014999 080000 060141 297129 844295 948553 052326 974865 550738 309261 296640 148329 489446 873634 027127 467030 736529 240086 947284 060779 145503 728958 607869 422248 003037 510861 365820 375923 228135 636532 861558 870775 778475 / 32730 740831 104864 713150 063473 608117 703113 669138 659184 392788 414633 655998 613044 342108 798202 706976 384476 144890 256090 957852 563500 797873 480589 180409 685147 618785 129841 219903 217107 548903 897610 312288 480125 319993 708719 623732 380200 763525 191576 736616 723545 436462 331910 018102 358977 008337 323717 383372 646825 842494 182039 393579 238244 866549 360388 792750 008782 577022 470282 441857 671242 014473 678175 366169 310622 755693 693435 849614 477681 840204 747331 166284 098506 440720 223251 662159 060407 765505 509963 962172 423996 814303 987414 244241 342051 125063 865509 948270 115177 459450 160817 319730 324925 233818 466841 886609 708614 662026 717491 215828 306851 061087 986857 489586 280066 075499 274350 897546 122506 133086 906879 230170 600476 784125 834487 939121 118307 542430 499305 667239 286078 490018 400733 270424 969570 094213 851769 057604 692002 979103 087884 355908 299761 112595 354902 273307 542909 323722 151125 695286 863833 422893 362352 773784 432491 145378 998555 225127 686571 227842 204377 156418 303505 911633 > 3133 [i]
- 2 times code embedding in larger space [i] would yield OA(3133, 300, S3, 75), but