Best Known (28, ∞, s)-Nets in Base 49
(28, ∞, 344)-Net over F49 — Constructive and digital
Digital (28, m, 344)-net over F49 for arbitrarily large m, using
- net from sequence [i] based on digital (28, 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
(28, ∞, 1441)-Net in Base 49 — Upper bound on s
There is no (28, m, 1442)-net in base 49 for arbitrarily large m, because
- m-reduction [i] would yield (28, 2881, 1442)-net in base 49, but
- extracting embedded OOA [i] would yield OOA(492881, 1442, S49, 2, 2853), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4 888444 473609 299769 476162 658871 541046 042404 043483 710381 722682 148073 761250 368042 310617 531334 668885 317752 690018 054973 951746 788636 877659 239149 456263 319643 245999 176734 064472 916460 645154 254469 616760 473595 394734 773470 556784 911940 088263 181736 558658 973481 260970 703349 823257 767693 156192 338730 269660 192451 961760 222596 769518 350141 336934 247854 692372 593665 232757 666056 404111 107282 254766 613637 675202 881270 805185 071077 279399 772745 551123 559971 334748 659123 219959 948756 969410 678123 132910 721967 307972 254064 922370 640350 895080 283930 216718 347663 302081 391102 481055 597509 794422 694315 389534 516140 831051 768066 640358 919375 029097 220214 506077 604067 334089 332926 855536 391290 968916 639720 093442 796826 362704 499288 643228 562523 841542 601018 960105 581180 684520 044445 961059 962069 807754 540755 468879 492045 993072 989924 364938 581155 240064 272494 266409 822511 303235 721840 675846 689693 880531 734835 194158 593695 513865 540211 620339 411741 673772 317912 540227 710285 751898 087556 471101 579423 363694 226263 802250 908351 915713 361304 739438 709827 446772 346769 893781 993957 488559 547302 879348 308910 839036 266603 097257 254192 399294 363609 994748 071756 693493 806409 895557 291367 815954 731792 645481 859702 499527 814837 687747 112532 986805 069800 774324 926193 998443 394062 595903 369711 115316 612580 818748 030691 606027 575242 605959 494552 556507 326158 544774 531170 111330 661153 607870 344295 919364 804267 889283 000354 749131 348288 185073 859003 171431 173238 008618 594449 106376 806959 634194 615300 509551 656293 473901 958134 607714 953241 594891 993363 277508 468506 736762 656570 034149 516588 832396 858311 287925 932606 560767 281548 905900 822674 802149 182533 341060 815011 461961 378242 895821 680200 760793 405964 420226 205349 658877 560711 707881 228461 213093 979024 403127 049941 377648 788290 084787 635818 089676 481043 332732 126016 640400 505351 449486 049061 631654 807902 077194 823708 347098 473555 113964 930122 981674 715449 808639 884224 999464 126346 676710 547693 532977 433910 932086 193178 030398 986232 810399 074164 628786 623703 216827 650461 106501 001967 302249 876822 107589 325120 990258 293013 125012 525336 141822 019751 263538 846748 397118 718208 847571 273744 089824 158889 751518 498793 697739 800610 775653 109184 597859 656807 178042 761024 233426 519155 926710 055888 777359 496631 055064 250843 604193 714258 594221 382997 400294 965879 433982 725517 544389 025808 406851 083567 717735 052653 562185 452105 382241 256920 814125 814380 841544 689757 162831 652130 047385 133439 457365 732842 877021 234111 491629 150038 679364 594505 976842 774601 257330 327012 603054 053676 301630 352608 919365 087998 205093 903459 600417 244564 349398 437148 826532 414623 788516 921924 446024 161146 494547 495427 310883 174811 598241 142638 692835 485205 359306 567646 221187 360855 785845 979261 566217 076785 701265 055282 179006 699026 841794 233423 701439 211815 041714 538415 945433 948987 774940 431252 015464 762376 550561 046460 949397 714891 553059 757220 864089 322558 541776 065480 712775 381029 446408 879679 227389 976628 029704 726631 444371 867385 339086 793948 024844 339293 926269 074374 901141 707880 987210 409914 858737 352865 786162 772104 978851 861940 002505 051672 172201 313663 008823 339174 447392 682413 790166 379411 695737 983972 238309 763600 307141 933312 382288 632981 612293 960030 651670 355092 477868 188896 669990 239725 407828 985669 295650 560093 656108 234540 919143 200238 443235 718208 982721 066442 010215 300528 319180 031545 891960 926168 774692 713799 218973 650035 199136 422087 429156 310719 678230 574636 614870 507335 721906 904457 616430 919930 002314 815641 838285 608492 560802 931765 177326 513843 294349 516087 844790 122902 303203 438345 753693 269557 603786 740663 346455 641090 953417 344792 060749 595136 984904 297340 983286 048397 202812 530282 458124 615823 121226 579873 237130 764531 484419 650879 551163 074167 516137 714118 588537 953778 415758 712205 024963 114566 087026 007163 477386 679712 230322 413012 657437 009780 830149 305614 802878 444750 875205 348434 459715 267904 171676 856126 485398 272589 263829 924566 489623 896174 409961 354052 114039 518849 057827 625734 758094 325707 964024 736005 728432 680348 868296 998132 738883 906697 264896 588009 082895 141876 305045 535022 231799 228887 415675 260045 721876 564272 961498 856453 122557 081379 706942 583809 580963 807325 412421 815271 371098 221506 759592 915580 968746 430046 213975 114315 545375 290635 738079 080361 498667 908008 061011 051805 162164 249087 076834 258981 274359 769673 865002 261814 550498 870358 530468 290267 254200 516966 053678 231166 106551 816601 541757 075158 385439 803136 335881 956418 149581 636460 969885 631665 371573 187438 162612 763775 021362 244294 100516 269969 069747 251607 372970 962457 234252 100328 879767 247945 093463 767091 377051 375948 299189 160129 322302 963938 220494 957638 788693 809932 542361 973262 218706 191257 061476 848798 227154 246060 118095 042597 874528 257721 794462 959177 557562 088354 780047 571113 233228 892653 591754 363697 570425 047844 347264 859830 014953 733329 919123 903517 428465 159624 506906 053513 410462 227546 737488 892105 517923 257289 091546 362282 278331 499826 404158 897979 067266 310825 522772 511329 666695 147868 425099 074429 555033 658719 355840 799498 056722 609038 855462 849944 791458 497473 493639 987628 159427 518457 930972 609938 237528 267891 394790 092229 167507 702154 461368 150256 337206 747657 740915 270546 270156 438502 175705 108486 699849 781552 137890 231350 384281 633880 249969 522553 044035 / 1427 > 492881 [i]
- extracting embedded OOA [i] would yield OOA(492881, 1442, S49, 2, 2853), but