Best Known (30, ∞, s)-Nets in Base 49
(30, ∞, 344)-Net over F49 — Constructive and digital
Digital (30, m, 344)-net over F49 for arbitrarily large m, using
- net from sequence [i] based on digital (30, 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
(30, ∞, 1537)-Net in Base 49 — Upper bound on s
There is no (30, m, 1538)-net in base 49 for arbitrarily large m, because
- m-reduction [i] would yield (30, 3073, 1538)-net in base 49, but
- extracting embedded OOA [i] would yield OOA(493073, 1538, S49, 2, 3043), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 7 819859 120088 902584 925945 024580 941835 284880 809356 374714 478147 534694 548096 301631 322259 040760 429716 204445 945337 767484 272394 549239 460494 585264 695738 431154 474888 210347 705366 723466 893519 110064 771959 571890 362748 966073 463641 931437 763092 233817 563850 280464 226332 383276 541480 316874 111438 454579 273492 801969 163167 627188 901814 158046 012678 393841 707155 528186 937045 077306 691736 579279 044635 924339 663895 028426 878820 139527 199664 041088 699851 369584 024739 542349 831503 121464 900137 576033 207640 184624 122301 080350 076989 248170 693033 969846 367782 449663 219591 106151 772706 800036 279879 789408 142506 843861 976051 679568 226831 107538 843215 124658 987269 833427 129449 367211 282759 696599 107137 470607 182208 415245 316858 357877 540548 355574 954921 181484 272502 816733 173750 883546 830841 193198 721647 638286 341883 384551 827758 182366 292901 731879 236201 308216 334764 292303 957794 813438 292118 307293 295055 996400 172980 585875 613919 299804 460233 551911 050233 769057 211059 583697 223045 754871 816615 214130 018462 219347 207479 645809 555378 847632 342139 857215 554802 209553 736068 468451 532194 290604 548493 235846 882904 877329 726974 275524 268233 632932 786797 412619 343600 857780 716067 925248 312293 414802 373101 901295 019339 114175 176203 419970 867905 082231 900156 342246 790773 443272 389017 765513 694479 671560 094079 839148 261696 135160 564606 525667 290621 166094 588950 876525 802264 513765 978478 269060 778487 237864 784759 319214 587892 237447 984666 299939 983155 507341 520068 619211 120328 615187 891873 076807 097709 002777 221854 711069 197683 230204 464208 881453 421707 702604 502739 149072 147152 471458 116258 907840 380014 832099 488583 460459 704097 011217 707374 950703 105587 019326 426426 439196 070598 285569 575626 300408 363865 866202 988259 501846 143817 743825 187646 098367 129923 771423 753322 064677 359176 641702 463468 837788 793437 244293 678999 291317 533682 086179 141359 005535 275170 192903 396397 198405 885527 423812 900475 201707 027681 531140 221501 444695 956495 270707 866781 252959 647838 091085 123220 977406 632701 197772 322236 655554 178668 443688 026208 840749 876931 080493 130073 576178 578275 895861 025585 310148 930317 412576 869814 212048 478730 832198 619704 884137 517553 520082 527643 074883 544091 528349 629026 272372 479078 282420 904840 070756 508583 563117 178387 706455 488530 757817 052186 634658 164538 705270 584453 045773 810270 508900 436203 087863 663206 707918 003305 314730 656932 020602 022764 600025 535194 775917 724208 716397 802625 547692 669379 824070 814546 442656 179292 183711 641732 635508 252119 403202 414689 604977 525140 678395 047040 382539 196765 843974 103786 585050 866183 837596 797959 371377 724297 324674 019009 695898 540935 691905 310416 974264 935927 476042 282688 718570 070105 204911 713645 246628 782876 686608 760016 750201 638637 177375 697355 167423 319321 325960 952524 551246 186579 480420 977136 790619 651891 808779 636483 048424 009246 169354 504846 826373 228116 258388 060152 883396 784227 880882 079542 187595 652026 012301 231265 702674 807150 873456 455043 555752 690776 528064 470468 552000 329402 445291 874405 798879 456891 948328 963452 503005 435182 551448 727379 438677 027322 417340 158137 143902 627011 442339 648603 785654 219319 721185 834867 622716 287638 085073 823033 353248 781537 763572 378527 944639 411823 204479 583108 372207 582474 983234 389646 165913 293799 106523 050372 997398 722932 393795 685924 689768 970890 030286 702864 743681 300272 972029 012306 372295 968582 682773 129072 904319 311113 453377 588102 549966 482356 732167 633776 334088 845935 150066 634683 127365 768018 892450 817608 608443 977301 836713 449784 770303 747062 026435 151887 884746 786357 930172 347216 335620 511276 505719 705457 459621 369560 126484 170844 038786 226268 945059 438393 086589 990599 770360 890841 492574 497688 260265 713860 929553 270750 046082 440245 924706 705729 841800 471461 038326 230931 108708 612216 938773 434422 659343 582259 174479 355053 899061 381191 779616 148175 441168 801570 887047 591491 813600 306650 713435 433899 459821 146310 833704 049540 204079 315681 738927 027469 877258 935609 252783 430822 928435 627612 671430 475188 996392 498126 873425 332736 098528 142472 402295 115287 657369 675156 057855 545165 307358 002384 092375 607373 433249 142471 953401 712231 066660 321801 628118 650292 232489 047474 027091 438787 266116 459725 507037 905685 837546 971246 307631 769092 984649 358229 028866 815859 341260 611356 860297 327999 646831 821005 954821 869207 669698 505084 350390 442041 791488 408021 593031 654620 126197 361166 263755 077726 561048 404478 717281 945187 349767 748423 465929 387650 739045 789005 315459 360334 346818 928008 612420 320294 899610 506185 526616 965909 484574 923985 546271 363539 896721 920062 184155 071524 258719 753230 008995 839783 072685 354237 273478 570367 850385 697308 212437 823552 510431 102608 786111 710308 381238 359151 707587 762008 460147 893267 848563 580487 382810 405137 721415 657462 530575 797481 928539 333535 105265 891830 490086 193577 652061 995754 121299 252956 957716 368694 277098 519488 409797 012555 016582 128957 680913 853925 240536 113562 650389 485694 484199 160635 848888 647785 463872 217731 624308 627138 887084 801771 583937 863652 122812 865156 311462 328647 690893 300128 230817 234540 626774 672532 964148 595339 689850 017768 478892 086540 521130 511224 892826 326387 815558 078255 344355 836723 019845 932946 115939 255511 806042 539835 345681 874798 833542 751112 016147 045379 640065 430936 805315 430453 104845 735843 525760 788583 613850 983271 685187 046060 674521 372062 357066 874793 122223 334381 902740 340081 436643 041483 430867 263595 388174 621316 876699 442585 347383 923171 914228 200633 967069 898489 851553 342035 942829 189911 191118 564545 707554 257498 201016 077908 400433 661907 197744 323660 038953 486213 974854 886541 836221 361203 741914 802642 170943 993609 197129 507476 658646 434878 457607 901582 046557 429617 / 761 > 493073 [i]
- extracting embedded OOA [i] would yield OOA(493073, 1538, S49, 2, 3043), but