Best Known (44, ∞, s)-Nets in Base 49
(44, ∞, 344)-Net over F49 — Constructive and digital
Digital (44, m, 344)-net over F49 for arbitrarily large m, using
- net from sequence [i] based on digital (44, 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
(44, ∞, 2210)-Net in Base 49 — Upper bound on s
There is no (44, m, 2211)-net in base 49 for arbitrarily large m, because
- m-reduction [i] would yield (44, 4419, 2211)-net in base 49, but
- extracting embedded OOA [i] would yield OOA(494419, 2211, S49, 2, 4375), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 60 341635 669348 696794 452482 831706 284174 946679 271672 376246 222390 469956 434580 475083 734055 949691 841388 285241 246541 354121 862215 353341 064762 598510 882796 249134 076025 754625 530503 330158 639441 237745 434317 310257 931444 749820 236806 886146 876167 349277 885540 031406 374547 283873 520214 511876 037646 089690 781578 971558 032956 962425 842913 643631 790214 593233 826281 275254 067048 375522 629255 009356 396153 692175 957188 586843 782668 719215 928154 349363 329592 951557 018845 420214 898233 513307 690738 004405 949847 364584 633595 371372 069075 334481 872227 354293 693247 166111 125439 494167 238683 195454 769318 454920 316793 691839 608413 946447 718511 115568 130480 897104 570449 973170 780100 444282 160003 890123 268763 266062 672445 843770 264185 147797 149916 167888 221130 979980 358945 715256 491792 588382 049733 780480 100049 723830 569994 746715 507946 819394 778794 040228 837490 013082 909070 725119 138759 625956 242068 020746 521499 126383 386762 337610 207394 659839 854246 783412 845533 025674 048708 786925 424735 023820 270730 770342 293955 855785 206567 168040 975135 668771 226013 180179 567513 786302 391502 089672 055225 443174 613265 471781 645080 835007 761928 962447 227218 294856 706863 615471 903026 047752 718373 176573 218800 006548 682122 640238 477160 584233 999325 461379 590210 501170 946428 747314 930804 827334 950452 626638 027080 961007 800196 556488 924827 552314 558160 679214 603945 451170 884281 728924 875732 360546 644602 727344 835639 281490 281083 912183 250755 473893 737979 456117 137725 435043 753369 388416 879567 889923 261197 965200 087416 290288 907028 360344 565985 340173 099889 042348 827811 284644 934239 263725 649994 908183 505125 164882 654102 439360 419245 983369 465459 261973 322326 504902 035615 265559 180915 674965 249010 422695 280474 112311 197005 039660 879803 986003 655221 570161 394019 930908 789917 254109 923802 909451 583683 221612 336698 768729 463739 436066 248059 356681 510003 840645 744840 596248 020948 507033 609912 735564 369891 960022 519588 802772 153605 593426 076447 539304 536016 762757 208371 907156 724763 427682 546370 361881 598531 639166 330951 034870 265614 441038 876877 836096 293553 255223 531816 474211 918920 247262 281054 046147 169676 349332 736770 076120 090726 177128 397890 453825 368811 952807 403232 725527 146740 097468 099724 023743 800985 175773 691704 401985 830589 916271 389216 071717 045016 210930 020986 529034 076598 796048 668541 216995 660461 284605 700028 135123 387074 657398 400103 633666 827558 928251 415287 743757 947763 090159 877008 411855 934786 767577 399445 059846 297699 577392 137225 628895 272840 745289 412886 694653 044478 611901 810475 125709 820049 160175 279946 973044 061689 359095 409572 558222 963983 608355 041674 354900 508256 260120 249422 728465 592048 689029 524532 090116 850593 011347 114760 130165 963899 226026 968215 521331 632302 859150 154947 517396 133216 215239 359829 737402 262053 805411 756359 928213 041946 037639 124556 538458 062672 073034 288781 389351 733124 088541 947607 005030 841068 845696 873001 669977 031753 231693 015794 647671 362173 978609 982686 420759 770330 675380 239987 157833 433874 830624 392382 485625 790533 612549 167151 570614 161017 732641 467395 521388 316547 766499 256398 650362 729841 738689 002406 889277 286178 397517 287608 426319 527929 313814 300926 624665 005759 282284 033939 441210 970429 824371 610530 796116 377806 790767 872540 986732 936846 415684 176185 312439 176440 270861 359783 300877 627100 645596 992982 504850 657424 196423 324046 864575 448849 881018 690213 687586 478262 499510 595423 892673 764282 698671 328077 997771 076728 270154 630318 315744 436955 654728 344070 756065 683802 128882 832814 565926 052475 176958 080880 486843 879312 481589 323217 193023 726746 580875 252466 647861 168284 218217 190739 118647 958346 890454 060305 849448 265361 550493 542223 847462 291642 721478 933327 108879 165350 612543 027006 595042 831506 099139 127571 113149 088007 726862 311262 100059 666373 000238 190706 269158 125188 430320 734840 285061 987207 926829 681640 786704 085565 731190 156911 366939 065420 055273 050427 324397 515734 626803 878954 465995 489382 281470 284848 716397 873594 925555 118937 196746 790062 821337 530063 564443 349147 008147 768529 059197 303093 139141 828658 001334 017206 878273 380392 353323 014926 186210 076485 148455 181671 330656 657331 971081 790157 860102 633967 468827 580011 331271 341839 170808 802337 586954 602724 985393 855123 915266 354429 448559 303548 988789 174246 006727 542269 477592 632713 100191 546890 807897 794855 833182 362729 881955 449072 360540 022390 217362 653306 330058 505315 446347 862287 655260 470095 001398 180002 706883 425077 134866 778479 034356 938118 828142 894841 223695 541773 381787 071559 514176 553168 827569 039648 143149 583260 460306 632222 854096 173717 180250 845758 493048 472940 729335 827478 744513 295509 571655 269890 588439 650104 380894 710654 881123 928083 734001 720874 552850 227523 831324 211828 697967 222852 852820 013151 595598 600364 023863 448142 865477 378557 634673 849420 397952 275635 895323 596102 238141 705326 974008 647165 665154 023070 129270 600469 315235 043016 910827 497283 682376 892414 129491 704326 188269 403417 820099 245478 586876 586101 252574 986914 936197 436351 485468 904372 008045 083195 983571 150359 228383 771656 591514 583095 056786 447404 753258 613873 441766 852391 248317 372994 535623 872854 947961 831707 250060 018319 675608 879920 822071 274054 499551 962674 360879 356435 136386 615673 833484 250172 232350 731444 958820 353699 659894 086015 407045 953699 427010 506934 999527 282351 130297 618684 463060 140853 517281 191438 817012 802381 134576 747169 304741 238945 169571 145648 860654 135641 265292 477423 718981 186384 392953 284274 013695 591176 409761 857264 140390 833520 961207 405751 555702 431252 230248 715296 358375 776123 210770 391942 295971 271302 977894 508743 442644 010310 343084 650224 727048 118207 664757 217042 499727 433179 824160 417399 509010 770936 127797 231841 245064 156586 654812 131627 493426 098271 398587 039313 700221 113071 151787 321649 693546 098783 698734 943391 772682 322965 140611 648789 253333 739484 516372 726744 912510 867517 443108 986777 368179 573674 881629 756024 904928 277112 657052 192941 939784 947989 290442 543298 286680 161289 156575 574885 475648 916802 517313 493358 008387 288837 039105 605108 578328 427325 417975 631391 489430 190634 089912 184312 698448 314978 934197 465816 585370 789360 751366 182578 097905 372412 781408 741723 592466 732691 150915 026862 235731 170258 859767 490193 074911 297238 081556 842646 479392 839396 240685 893722 110969 561219 615771 664337 273462 743477 862150 849339 634480 794026 020624 298554 134544 086275 182983 335173 747663 924219 226836 504680 015892 905689 277349 360860 184782 221769 758251 013497 472878 470184 932156 109836 437936 863371 630602 986162 737675 294907 484049 308731 942114 063063 402030 408292 117619 269169 076128 430654 410893 894548 577852 420931 634402 771062 635440 552599 051607 844872 887830 485951 663383 279013 494964 771767 708421 651309 266095 069526 554795 005481 100005 797239 346259 283538 859284 779276 089789 960404 348723 425356 541102 646968 980450 565012 138638 730561 735615 246254 612181 233538 270566 968819 210714 112276 661065 414706 611193 068875 378909 354726 147804 443932 650587 482797 624089 229260 235919 595436 448585 484468 900141 460193 573849 741949 485477 981828 854656 494641 885331 274436 420307 731045 649829 336469 138184 379323 159081 358466 880279 428108 644507 622754 038907 265009 884908 017292 988382 929232 422930 239687 380822 314374 475219 073782 604499 162878 018044 698276 358056 977932 784416 196273 096987 272124 621971 803895 704049 361592 702336 165077 615249 953240 574497 285101 984165 642679 832859 609147 251587 716402 013221 657013 483650 065521 710896 792065 030953 101087 193500 521153 390801 114518 294858 890420 844881 532316 031907 757388 375419 284111 074915 320696 488988 907208 433910 084504 671008 995334 200091 409939 269181 649452 463779 245532 403058 079569 553218 952054 287438 097414 273479 274720 995989 339430 606930 765920 784420 998249 482712 843133 855877 634565 746189 773620 975569 671906 302039 165438 475377 890135 120624 136621 701073 045269 052396 298946 003582 743993 794352 511305 740691 719864 349191 395735 479659 819244 037542 332712 067252 828804 324969 616577 571317 271200 999014 790372 052296 463195 184077 734997 412417 954825 609211 855730 368265 494784 824789 568641 297734 546817 604447 193004 777305 387048 937810 137312 377427 653355 118233 755072 913062 917896 663843 528195 057472 798784 210352 559439 908980 996270 552013 / 547 > 494419 [i]
- extracting embedded OOA [i] would yield OOA(494419, 2211, S49, 2, 4375), but