Best Known (32, 32+∞, s)-Nets in Base 49
(32, 32+∞, 344)-Net over F49 — Constructive and digital
Digital (32, m, 344)-net over F49 for arbitrarily large m, using
- net from sequence [i] based on digital (32, 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
(32, 32+∞, 1634)-Net in Base 49 — Upper bound on s
There is no (32, m, 1635)-net in base 49 for arbitrarily large m, because
- m-reduction [i] would yield (32, 3267, 1635)-net in base 49, but
- extracting embedded OOA [i] would yield OOA(493267, 1635, S49, 2, 3235), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 105484 228558 013522 052403 078586 744862 756239 259668 550671 677976 186626 955137 301225 516797 861612 547668 531245 178401 004399 953598 915164 818279 913740 034250 554513 749868 165160 354856 748462 379454 919633 373782 779085 680975 768259 063068 444743 249086 917629 030258 713287 007955 917586 997916 844914 819585 304857 160251 700307 375812 011426 136467 972111 366045 849415 307515 105910 237175 067000 536339 895364 498609 880840 324997 267354 007311 471667 807469 815906 392665 387647 129125 451132 334874 564159 291764 650532 187668 672742 801441 696879 592109 089314 214756 941934 286054 326277 633653 938344 454584 744357 812105 637695 286968 483965 702900 866985 113974 098432 630345 000923 561892 855497 758459 468693 634131 665227 416510 943500 747679 299900 706353 701171 385994 506825 080306 144651 701262 972235 610420 280893 578972 006546 212179 445614 905188 450468 993202 229884 595567 962651 324708 212496 636105 356939 141980 957316 634285 657470 306220 917577 862221 914363 406210 236853 949791 951904 794368 181274 726875 439598 762084 781759 217727 695190 335665 356229 551382 708123 665610 875141 980941 947728 706382 481784 865657 954856 028200 400611 383699 030893 526847 194304 701375 038150 400649 082738 461932 122090 741990 458241 858335 915610 341266 174060 694752 823466 232826 569340 338914 426847 173928 533379 571474 640432 534721 571539 789459 801538 840066 298060 840683 470179 789230 960955 602238 049806 572159 806821 243754 998789 817872 387208 902524 232360 470214 362405 563583 647144 335784 635827 257242 552659 526644 136540 087325 263796 128131 806407 875060 122462 146291 291726 625320 680617 973461 441913 351561 612493 441535 868398 811328 944707 168852 736457 213384 276198 277734 513649 158209 798648 029797 201234 387558 910060 278343 485680 825053 601868 275465 530244 943670 772940 940486 165120 059064 576174 505858 933409 152915 046905 752518 887799 337331 917151 892697 331820 174422 393099 729964 761402 668640 963940 155364 259350 093099 219418 005293 439401 815834 805391 861155 091544 313465 244260 285642 345805 572660 973521 668606 338082 336398 339225 148095 916005 258152 126107 159791 975120 390410 153386 832650 313429 341342 414700 990033 184981 747578 099771 353005 111038 774340 566499 097387 601447 179361 367253 814651 176102 338869 898047 554656 974376 314697 469168 834256 362667 954847 984046 963188 979606 573340 598773 673271 212649 712584 504254 871195 701025 976963 299406 269293 885412 177316 931879 899827 911500 271745 896600 465193 746647 750299 021994 138892 903092 314677 370230 107929 937634 812263 168647 549054 265770 863124 093776 168066 762710 709212 163299 647135 397791 598509 036855 685469 518323 721955 845650 979770 709535 071172 834874 423209 881252 972164 768447 057014 973168 781695 770072 756411 973741 312579 849628 301659 385526 684375 400504 105065 865572 255945 216952 101364 980084 871421 264251 787913 746592 165290 034030 801060 089241 807791 846067 279233 531726 903880 064395 606945 742231 637647 339438 372745 999913 533645 320414 441458 256384 451983 444930 489907 908918 647988 413985 595382 534102 163007 647587 890133 516505 381213 147146 124226 751879 835585 707044 301680 210735 594298 917718 876558 269108 999036 455079 763582 722981 408751 398453 651964 745106 643635 659513 003237 040985 993386 197019 280315 635920 488608 301285 937328 038368 446218 366624 558603 769347 453466 058265 078467 813349 729924 999247 531578 429494 087721 486324 357380 419833 461980 186935 647751 075394 469591 958746 364739 459762 489608 729572 511190 832881 643755 056532 759502 285481 429340 527084 444103 955099 177146 853574 192470 371661 097731 686484 069511 072982 341154 494730 418905 058416 138433 150493 812760 619005 461854 177155 827174 553680 583813 399273 871162 294763 288007 614669 897791 524206 690512 248368 820936 680020 987922 115608 773033 589231 418628 459846 772103 242865 321682 392308 514063 604136 947827 159301 343280 897602 141166 118603 338832 842857 548687 896268 851766 393207 097433 446783 085559 166634 031237 870114 921898 345375 163588 518637 489476 611708 419301 444296 941006 591408 148329 444005 495491 008566 784790 841536 299694 863417 208145 580684 750626 378407 748774 411042 754170 118432 068835 206990 373244 033618 530583 438735 278333 664322 201382 601074 853619 188745 129582 533410 533597 075620 836724 316511 845475 192101 916161 771911 834007 502284 447932 042865 005956 766541 031233 430783 741499 223998 283188 573718 604892 247279 585190 480622 217770 370537 411063 158864 317369 246178 198070 752311 363298 765051 471302 783604 199571 884745 676809 963703 032660 483521 568063 592102 675540 684962 463059 362105 936087 126723 681699 568149 296478 405126 877961 368774 066790 422823 088207 943229 825802 859155 837859 238830 743005 742582 790792 772273 756733 334452 145221 855015 736804 395639 420528 414612 079804 994004 022823 015849 335818 915862 686326 383602 507868 395143 600205 913974 049580 910336 880496 871864 559458 636613 405148 595665 074165 112509 147590 014773 812418 455872 950884 345297 879225 541782 590211 421549 648781 438540 586934 037043 541807 033829 562789 561628 704404 384524 997465 360734 616210 717937 479768 483003 373053 108755 333038 968468 023329 861152 100119 098039 724326 924500 704930 425000 694270 613032 243037 634702 178796 951565 078063 066004 676194 844667 650539 789164 895437 135397 776399 211638 007325 088077 921809 649864 498352 514405 090600 181235 387768 238480 731095 392223 879257 779155 822002 977326 768836 171014 220674 257361 554038 520917 477955 948049 949098 980623 778165 695029 995334 939239 623284 922542 536367 597075 298842 324609 034020 736998 193591 030883 570540 423928 522565 565359 419258 416631 823757 746196 939669 201920 379022 662058 379046 900401 310607 803836 422558 243085 843361 113249 226798 631290 307635 023110 561438 664938 302414 959218 011962 761076 223121 133394 116868 841366 881893 552761 340884 273379 921864 827876 601927 691953 130658 081232 894512 826737 107083 888406 427896 453881 351842 459005 960160 781037 929715 390841 886662 206470 672087 190853 904444 625320 387340 560952 036444 918243 873343 162615 797570 776576 892129 531530 618097 863904 922357 140501 167294 834612 090891 998111 822179 006008 779844 625992 660338 808440 018312 665723 391706 831484 086053 136575 961389 127554 822070 733526 085525 656344 533616 812981 770923 919179 276425 363255 214471 530850 281931 901358 460031 166429 / 809 > 493267 [i]
- extracting embedded OOA [i] would yield OOA(493267, 1635, S49, 2, 3235), but