Best Known (39, 39+∞, s)-Nets in Base 49
(39, 39+∞, 344)-Net over F49 — Constructive and digital
Digital (39, m, 344)-net over F49 for arbitrarily large m, using
- net from sequence [i] based on digital (39, 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
(39, 39+∞, 1970)-Net in Base 49 — Upper bound on s
There is no (39, m, 1971)-net in base 49 for arbitrarily large m, because
- m-reduction [i] would yield (39, 3939, 1971)-net in base 49, but
- extracting embedded OOA [i] would yield OOA(493939, 1971, S49, 2, 3900), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 25 702881 281912 012197 004802 119847 061446 507723 930949 795387 626411 785916 453040 524880 737499 921088 682390 103184 622500 104088 551297 493134 228529 656722 550200 553319 089727 419822 414407 795507 445354 787862 964643 660741 749210 869617 022755 423404 429978 699880 351574 667255 838908 655707 085669 890798 824608 663238 973436 993270 950577 152523 677577 423286 474574 465039 125542 453603 723333 850276 484330 013813 126454 196979 189129 095533 193182 032719 789929 799900 073407 716165 923186 857438 570206 430402 479553 293065 075758 671747 806333 720334 559751 894132 375487 446885 239335 363001 299374 315310 646858 287096 000644 316976 030126 545775 863858 802800 589381 700485 757881 358945 136656 196742 692195 206283 728501 688394 055435 362844 120266 516921 585618 800385 059545 935293 459515 572771 309456 574708 525469 750568 536413 752378 936486 997013 015130 936775 915443 136232 368736 581722 852761 513483 477364 670636 477627 124084 854824 873471 948317 043564 243568 655250 008609 329971 389686 832725 882810 892133 810334 195023 784442 185632 864857 432347 852877 345398 912864 946064 587031 762873 104858 643357 713736 488246 136007 432106 587688 984239 854940 903518 815714 131793 017643 602678 522265 288262 965713 058326 098676 282751 708271 631718 399572 932538 154375 422396 187373 651216 705558 808439 267180 695275 733987 356077 190307 001990 889771 382146 900256 119859 873986 601271 267652 453736 817168 644718 689935 956705 023325 007572 828048 781033 360007 384149 628577 576014 942778 243988 604204 266017 358212 226062 516078 049963 291236 496144 621024 002870 424797 284784 287967 845692 370125 514831 723581 017190 174252 761853 867608 886880 366691 394240 747201 454379 078000 083603 432536 955182 659483 239998 379014 285098 864097 193015 059574 474117 491806 937831 184470 043791 028218 286068 824202 478051 009596 236130 898281 023212 655608 483743 677847 794132 397733 829110 176681 792154 876027 501989 038249 539295 771868 726511 606402 052342 405721 706046 633419 682465 384923 801433 034494 759466 908937 947155 499161 100709 836814 423385 887688 774724 552275 982816 062278 687469 983210 825324 684020 378793 887979 359267 254257 855490 359309 791026 911272 260418 138794 587954 070524 320705 232406 328880 130927 982539 718953 016502 101115 396506 549531 437386 643076 127640 971591 518606 534859 141011 787943 279412 161909 167943 998690 714415 799345 816866 254828 761138 065832 143113 182506 149054 576690 610563 474102 650480 778585 632833 050361 102261 050258 672370 083419 817509 075163 636420 244064 233486 184618 378285 260617 682624 121556 753912 142753 665615 942254 784906 632195 466338 724442 165224 275569 307354 866097 293169 137949 069084 456249 310016 074839 850517 764648 606200 393483 330731 115941 270595 660004 943407 064734 408057 261686 830572 817480 976355 549608 851110 333844 802354 213775 165166 319904 567360 636296 177206 683179 390483 323327 354911 714448 569772 673817 888567 548182 520690 193213 199002 121525 054934 463283 342374 513683 053516 054417 764486 609360 394888 009966 354724 835699 641538 541687 040247 429021 833005 794116 538435 478627 525974 581789 155764 043423 788362 516962 740492 317441 771788 267332 399561 179609 190986 663420 962983 954464 307823 362126 607026 407262 215381 178047 722508 165108 649305 444129 728233 215150 917760 613227 768736 076985 479560 847826 943669 547148 221136 281613 974625 663334 763280 036684 902356 617154 247333 134332 656485 889672 553701 297797 043465 308274 773377 200906 259946 960546 614457 993357 213347 697299 498453 193119 615641 894262 131536 138421 583230 384826 106275 466002 842709 419359 977810 534230 500090 280355 126359 703833 553053 298103 754195 905049 234690 141758 493697 231655 583061 700828 124912 286279 742193 212325 118218 229540 769555 213531 575985 382909 777654 473365 524837 594401 042540 853076 995060 627153 720490 149271 273510 530678 681945 851880 611421 795971 587747 594953 072890 485004 856882 795725 914526 271469 929113 393403 152718 087774 300558 881491 569488 765387 751959 896290 214726 871865 810089 947400 185913 086799 938376 862989 811128 406564 301309 311682 791816 211832 958580 318925 174654 675201 699600 238317 233780 453767 924856 090958 474128 572207 453293 847170 080472 542020 421225 773489 677610 584487 293721 579499 913140 064422 823569 332468 603048 728248 971518 625782 161064 746731 799643 957092 833179 171790 194350 935032 643705 534663 151865 090445 630321 804241 659212 131661 998750 371634 513582 112831 692439 992667 969136 646570 846729 145280 393325 700473 313705 822034 155816 018265 899472 550638 712826 013486 917210 755113 261464 581154 453874 132265 863294 068475 552131 214944 500975 833545 124507 153521 970086 307526 841112 135428 903538 303371 326902 865253 815029 451966 517649 964982 441472 476107 744186 415767 190536 883728 736067 311329 288232 766981 171853 393094 253797 632305 441624 456545 606999 117729 720621 298034 090891 656409 583918 730804 194703 283276 173817 808942 140319 113171 875790 438025 135114 749761 113880 729746 601707 125688 668968 740649 527341 672875 071266 876364 408384 489630 006034 692270 497596 449665 577470 394459 652381 929448 278084 251556 254775 039661 168667 593828 675111 743308 583065 815581 317410 199162 072159 472266 855350 190387 094122 636521 860231 021089 235826 871260 691444 230473 148054 087387 518594 642709 500043 727008 693862 031404 311664 482161 664546 871206 759204 262890 274181 931979 902252 353051 795148 889300 735473 201621 158974 128596 270377 510739 802623 723840 716768 786872 927008 268198 442847 639386 241282 834266 577056 102613 330704 259305 516649 560013 037459 464529 512980 205061 559037 188408 793385 648556 796697 251297 965928 747781 804042 501655 153663 353765 101918 510563 521609 090318 359138 696501 740602 611089 497766 889741 451323 506777 606147 883085 121382 145236 591034 275722 015875 187798 721806 793116 054718 673121 364600 415703 488736 366744 556782 843371 110289 825172 625656 816341 573828 405322 862394 024889 581157 713554 872076 058976 414715 817330 149253 271968 184187 289827 981864 531637 386116 281512 193545 045540 525852 954473 572545 736818 686035 794061 082327 853206 979622 352438 702234 029811 897093 830702 272680 477529 079941 810393 871543 603264 004797 488648 639739 372305 567295 087866 368607 604182 264315 554581 282530 163029 036891 519717 198486 698447 932607 546735 253518 514132 759386 340789 015949 403983 448596 289303 318672 395638 890640 740558 816985 290392 978928 496786 013723 335199 027106 503439 997854 869472 477289 009617 225263 159865 696776 275947 110639 379972 974439 810672 392721 921836 447441 060153 993951 468582 041298 635287 469297 037192 880080 740955 960702 093894 397081 755527 190164 484013 920643 959212 833655 355864 544363 181231 514150 920700 688986 306518 433732 309643 600444 744098 608285 206707 222356 337431 861302 789896 094839 566984 804055 455174 883443 810487 600538 492318 858179 091588 058414 985112 944134 332440 610875 949618 280830 103322 742160 132403 129300 163208 685909 082414 441402 027745 839698 913327 043506 442583 103833 177631 609426 290479 609737 920308 131136 182807 362834 935280 463490 141313 068999 995634 320901 767977 150924 183540 505837 376495 283560 459744 297240 598800 259302 777279 223920 636084 728243 815485 890395 810912 216215 511229 287987 993184 945084 482242 319546 914388 007816 648214 105827 520630 037588 298482 215504 426367 205850 448412 813592 869366 594463 489875 179001 281285 506855 032208 721598 403190 192388 523985 256466 302596 386833 072312 102954 421209 892355 939457 736613 766945 159924 265110 381513 443495 415348 593476 632647 483722 218345 978498 040647 213909 565893 654562 721607 566999 662472 858305 491751 947831 381981 987577 338860 952109 / 3901 > 493939 [i]
- extracting embedded OOA [i] would yield OOA(493939, 1971, S49, 2, 3900), but