Best Known (42, ∞, s)-Nets in Base 49
(42, ∞, 344)-Net over F49 — Constructive and digital
Digital (42, m, 344)-net over F49 for arbitrarily large m, using
- net from sequence [i] based on digital (42, 343)-sequence over F49, using
- t-expansion [i] based on digital (21, 343)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- the Hermitian function field over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- t-expansion [i] based on digital (21, 343)-sequence over F49, using
(42, ∞, 2114)-Net in Base 49 — Upper bound on s
There is no (42, m, 2115)-net in base 49 for arbitrarily large m, because
- m-reduction [i] would yield (42, 4227, 2115)-net in base 49, but
- extracting embedded OOA [i] would yield OOA(494227, 2115, S49, 2, 4185), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 10 670977 154920 526524 028490 291269 299817 215652 261527 501372 815838 388335 664283 303283 973727 592571 399542 679740 044727 080527 308921 935194 533232 513228 199809 759350 310252 217044 063943 128493 996557 199194 624461 701456 360825 901429 921039 281945 203297 418047 543995 586724 824345 054160 067726 160043 912534 260827 588915 270561 575607 649450 993757 582551 631264 145647 000549 977548 942359 381767 784943 717951 727952 260356 033357 996051 811487 667030 949131 429942 605268 924134 934187 307243 526589 474650 271308 975920 743886 854418 815181 775052 625673 269764 476640 395687 683305 763546 736209 236136 835145 598200 184782 543056 565797 298926 055438 794763 155451 512427 046727 663194 325725 750551 896157 434621 709656 545563 247879 220802 441546 396151 725288 881555 525249 495978 855821 365867 957637 691432 383709 939508 709589 723315 825330 131397 748040 246408 391262 550366 178890 066293 440517 435442 862308 304536 932214 942631 870428 758900 191631 139633 261513 141487 435418 018404 091648 326625 202095 159324 448456 538469 832806 608538 016366 847942 740991 342367 817587 112726 820631 968899 064167 411772 685783 471239 161430 837936 823142 981328 008774 654891 035622 703110 880629 770456 188834 603101 856548 326075 612883 828685 763013 205887 469911 057680 544490 049829 024987 513309 500536 289591 245408 000567 617301 689462 942650 661366 524041 481219 899106 736700 204967 503774 652171 345102 252017 961073 949635 566834 402606 489648 448909 078012 148655 699469 384926 634906 174360 741318 419437 460515 691793 727768 468570 902266 649230 778418 289863 056511 829943 092603 942114 395460 643748 544171 121248 109605 710184 236068 623381 161004 146202 186742 806860 820822 443297 302277 383343 737657 803044 331694 817108 296938 645116 888904 356372 014198 816405 049732 587978 719760 624453 081337 758906 527214 724990 349561 461455 833367 949936 390281 033153 618546 464981 882362 224984 672602 816449 259765 093838 605784 844785 415958 981146 888866 155397 110795 582110 360430 994397 050358 974629 736067 735647 908010 203623 956408 416235 301674 438973 810594 122849 934166 560205 840652 594582 035639 619799 254116 764471 579406 123425 227260 884678 797537 835123 614324 424713 796504 396751 358875 304257 419566 715905 784354 824046 695660 644049 839270 896511 386733 784388 092540 704298 281508 330810 126976 610559 416681 955002 670103 104836 421074 519839 144305 796419 267216 491577 183212 040572 480196 109180 238682 275822 168633 840087 802987 548357 784885 037275 407413 192030 057663 363792 130094 536574 922726 775902 730490 678618 304043 950418 328564 774726 041977 790580 665400 442431 632628 668120 424308 214161 947843 462355 553762 335210 691482 846145 403415 173800 251816 472008 054044 442313 242153 279829 550805 927420 563108 743334 777668 908955 445372 554335 137065 221809 426551 075989 010859 265650 841046 509066 572977 924052 387170 634777 620596 433229 496136 517195 738131 261351 397263 658718 385750 869185 388253 878340 510712 688254 618364 910587 824695 997142 295231 283219 234298 824310 902637 031060 044498 095458 506570 205438 646398 687304 242289 825818 378390 075186 632182 800876 413281 793330 854827 061236 518956 869360 493452 897579 461716 393231 116010 984200 674320 713145 659349 916483 581853 048895 912126 358648 957049 404898 770764 540973 063169 522792 313282 202924 780942 145363 919890 647225 961018 722386 709079 332540 999957 830476 762922 685369 060908 417914 261723 068175 569511 396732 361475 870224 689007 757065 816078 911055 645355 508532 341869 078381 262555 159227 160937 925483 797749 326241 760156 151890 668552 772797 149248 402158 110087 638429 483458 782210 085113 801589 720472 347895 108869 968559 662459 183399 155725 218489 714643 315362 931644 493325 229478 113056 673397 358727 834358 894714 244100 398821 526665 991373 971153 279269 035935 406747 012215 602358 810809 628164 305508 168475 390356 443872 571397 075758 840972 065238 547919 832791 809253 082295 963080 052864 489891 807270 284791 979628 263408 381302 168181 770030 170015 166871 085853 933272 772796 466949 482180 626775 902957 088693 377266 036699 765317 656371 938800 712732 361765 384876 188115 112026 825323 269750 172929 754436 979258 118822 400556 064585 136296 853667 861936 194804 439585 996642 232651 688332 411596 381236 292183 255679 055605 029128 877021 457656 282225 388873 864747 573990 985430 972162 286137 776948 195761 146123 940806 156843 081722 987337 102770 837191 005645 142799 620867 181050 950425 390998 582139 958498 427727 196178 240750 523421 025271 073512 080203 816931 389254 923002 909185 290462 166718 855315 524658 869756 727707 831442 579849 765804 529543 301263 580005 596656 710018 985576 813831 443064 492339 441644 366622 082312 031068 486297 127969 359863 897427 460501 410983 107758 607721 009506 867104 250808 550828 455849 637058 516198 417680 524734 065277 892971 535087 649845 669509 448616 936418 245032 754430 563517 903128 882133 190810 562095 937957 901531 877367 611290 265703 347262 082782 230797 312616 399108 310767 863603 230762 457887 919117 947160 104749 459539 424704 020926 502743 782311 947274 165975 165149 474012 551948 036907 600025 067773 926985 963162 905702 299126 227736 708217 101537 425702 158332 755967 562369 068252 946077 859292 027962 884300 468517 479585 665721 116002 872191 428614 172050 251015 130049 838326 695425 836660 880055 211373 982089 494877 091513 285215 786641 178763 973530 498209 903203 242806 952231 200110 435392 036508 089219 678317 547109 816829 570715 568542 598774 092502 430743 238129 386292 776420 396309 574074 282090 519903 722699 950864 367127 945735 607830 381657 070742 895742 464873 179330 486121 507600 259218 449867 561814 197138 397206 708097 711976 711746 455996 135328 419035 076948 576499 874885 043752 487668 551281 978264 512928 108031 988086 766648 831872 121066 397076 160415 558194 689871 279865 805321 482445 821954 433876 975416 890687 526468 598673 622911 201253 737163 086538 982548 019879 536117 531927 729755 938677 017338 377047 048930 986490 752168 467569 224765 440868 495410 971851 858412 338661 350477 444213 634622 669472 305249 798759 422203 058735 936707 312758 883276 751290 126369 525763 566457 358553 912556 162848 860164 271202 838936 563937 385896 147550 769587 452817 792647 640261 414493 386944 018204 363009 587537 216423 486596 066749 637816 626093 364911 661403 049969 912327 423706 413110 637038 710444 146594 602207 690955 345226 039077 783420 446382 720729 789509 809754 499586 876803 967711 858888 202770 100989 762757 097164 719599 311554 559109 336584 778530 530897 528176 450097 220124 160385 830878 513904 682262 039946 876409 403732 274894 146325 318079 651145 047785 650753 898620 133742 879254 064086 670808 328348 554474 157165 382812 998733 268838 087216 027379 924928 185410 764565 395884 385306 570297 526935 544320 716374 691891 664355 221378 510769 659367 381912 518339 876605 498279 345811 169509 340763 686627 725712 838644 788047 205609 187506 145894 018779 082209 487646 341349 553996 160923 068169 176758 021371 518154 632447 054618 419319 588218 156571 291015 133139 866264 876397 721436 022146 326081 177991 345887 449327 714343 053928 122678 164769 510501 782414 918119 539679 258793 623955 519224 376689 203645 052660 243997 447249 335786 438121 391142 721793 717956 686278 131020 966704 794638 751386 779593 133936 162512 702611 030908 214799 752411 473180 119030 735100 662474 053695 142362 832486 193771 685180 686234 846510 867227 250384 514940 306872 293928 660001 025948 684237 577499 563688 279918 625468 325230 935842 301038 606716 757055 973713 053410 269892 325026 080813 948009 246153 345537 405791 596638 026819 229240 046638 967449 660408 760316 980145 820348 644644 691464 649092 536981 226776 502197 761967 152982 369851 691657 541606 888216 144215 593321 263716 968395 367874 768514 622900 174743 224986 834434 772910 281658 272158 617710 047309 454913 484919 871148 387118 490040 477022 692540 896871 113482 610847 363076 247927 118302 230138 506327 784669 268124 251634 245095 736052 181197 817901 508327 673968 120607 866945 503675 302580 726087 022542 961081 703538 151721 592043 841662 758104 167290 644679 689108 146632 305013 669414 281473 620088 430186 169629 197855 410010 934351 171396 994521 164516 940348 209377 233913 938023 589758 391668 758041 353585 523106 482979 / 299 > 494227 [i]
- extracting embedded OOA [i] would yield OOA(494227, 2115, S49, 2, 4185), but