Best Known (135−78, 135, s)-Nets in Base 3
(135−78, 135, 48)-Net over F3 — Constructive and digital
Digital (57, 135, 48)-net over F3, using
- t-expansion [i] based on digital (45, 135, 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
(135−78, 135, 64)-Net over F3 — Digital
Digital (57, 135, 64)-net over F3, using
- t-expansion [i] based on digital (49, 135, 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
(135−78, 135, 297)-Net in Base 3 — Upper bound on s
There is no (57, 135, 298)-net in base 3, because
- 1 times m-reduction [i] would yield (57, 134, 298)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3134, 298, S3, 77), but
- 2 times code embedding in larger space [i] would yield OA(3136, 300, S3, 77), but
- the linear programming bound shows that M ≥ 2 877497 892950 766500 817281 802603 936483 111586 892961 745454 845292 822436 985813 492157 631230 907855 668983 481567 196521 798483 857864 006442 434178 001274 220434 457127 083884 241053 893634 643025 242466 006246 586087 802582 797098 066246 853537 664790 169398 621136 389836 350963 473078 858042 210227 541817 012499 255433 530293 515281 815078 570439 340405 668463 731819 536132 138731 104041 454735 941346 496749 214594 944597 059708 086730 318638 850677 054729 660114 994135 761497 196912 780186 379608 259338 148919 561286 052138 341426 113188 139227 743837 838645 574031 324137 901475 459837 443763 864895 882881 268341 534124 810648 306383 220393 857350 834562 396467 130295 884013 554082 351163 404856 250491 657152 124953 868822 105397 633907 705140 699694 395995 688069 572180 075527 068303 756240 739843 772826 348321 781102 813825 475554 599172 100283 960358 907278 324383 768707 465841 506222 170330 325354 294968 578041 214880 210608 849066 176229 012593 135594 239587 747224 780033 421069 118397 592011 440496 393558 529101 976371 785768 930261 490391 051310 102656 694567 752436 576341 594756 512486 205593 982727 232136 066348 619580 511299 637651 574484 310622 790372 203960 190055 618846 079366 760550 129029 513839 649580 978666 034157 826526 877672 396337 602416 906209 238617 055859 782183 624002 036785 525480 / 28 407238 543415 291638 769916 484267 491419 957188 928032 063233 366764 631283 778817 943579 435921 166625 792928 456159 909385 963298 449946 282826 584784 905022 685756 607775 511109 947640 761299 778309 311537 368287 439921 735484 070562 709313 105710 275662 308305 144922 066277 376751 909636 325274 719864 410270 639839 667686 486712 582149 224612 099543 830520 988971 012263 602462 696665 199289 623959 514587 511127 157155 615346 472370 040425 307300 375598 579167 983894 465745 500723 093126 696123 882924 974670 325667 543799 465955 366798 002989 253005 180454 251060 964560 882658 656247 764619 819272 943553 170695 888761 791991 945404 466599 343703 205907 621162 707542 503090 210911 232044 339712 144129 059261 135064 528222 233131 866068 105854 472215 284526 434694 053135 258354 787778 058228 911150 097826 453440 224429 293389 889193 740094 175375 085070 422452 644110 457566 390101 782519 578544 530007 879228 775974 407558 442162 326329 969708 184369 575079 491498 623106 034870 228181 692966 386504 453231 412678 770245 628499 206031 021726 538237 463317 879499 428900 383521 151487 309950 867838 006552 753681 157309 410838 219119 634444 703704 297638 795228 771642 849886 021340 351479 220975 261181 552193 102371 799201 926393 950581 236189 > 3136 [i]
- 2 times code embedding in larger space [i] would yield OA(3136, 300, S3, 77), but
- extracting embedded orthogonal array [i] would yield OA(3134, 298, S3, 77), but