Best Known (49, ∞, s)-Nets in Base 32
(49, ∞, 120)-Net over F32 — Constructive and digital
Digital (49, m, 120)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (49, 119)-sequence over F32, using
- t-expansion [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- t-expansion [i] based on digital (11, 119)-sequence over F32, using
(49, ∞, 325)-Net over F32 — Digital
Digital (49, m, 325)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (49, 324)-sequence over F32, using
- t-expansion [i] based on digital (44, 324)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 44 and N(F) ≥ 325, using
- t-expansion [i] based on digital (44, 324)-sequence over F32, using
(49, ∞, 1585)-Net in Base 32 — Upper bound on s
There is no (49, m, 1586)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (49, 3169, 1586)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(323169, 1586, S32, 2, 3120), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2411 771314 849045 592357 021965 757728 438469 327231 437595 957657 159726 430427 184508 637661 029028 029870 868697 808758 245761 039467 150374 828786 540156 660049 861520 177619 110478 954468 646079 556373 206496 542576 557677 312107 325108 456023 261995 504110 573076 627704 656158 232960 888578 224555 551242 251189 794256 147340 085635 226087 421174 990456 153309 332444 318618 255039 627592 472878 553535 012657 293558 320238 474957 909622 836399 739894 382544 229575 671116 339855 390642 914195 112590 826983 233220 751482 123428 499362 795528 283203 830132 380303 834347 835942 212923 359634 415821 664016 308424 111696 490629 975770 123274 073610 633271 786151 509100 130541 528573 339257 311910 690555 403315 273536 029531 069914 206767 228352 485808 059261 535829 754963 550303 762810 279669 208412 418453 020367 434537 321871 976034 502998 573442 719547 514124 931797 620944 526292 267129 615885 553741 094567 121302 142934 149548 107931 420744 129925 513904 716530 585931 424653 537268 268110 849620 698044 842428 705584 470712 145164 334125 369337 826322 668466 443678 394348 577512 927984 651940 664383 692406 019878 574344 355311 464249 911008 189371 604450 118871 700760 592767 563536 558664 792216 670614 610991 092334 582966 087878 266371 302232 418220 227324 442044 602224 757903 152453 358571 246100 576115 034644 562636 426402 948350 312145 477272 744790 101838 960793 168242 386658 892237 559888 024798 479544 271401 950746 016496 876062 950563 150130 963405 533907 864158 442872 060220 323855 229759 856332 939698 993490 993970 108814 036845 804761 304640 703819 788474 346051 186427 535816 671032 553997 369774 134568 235460 327232 711758 548156 599497 573965 562949 221144 913161 145675 314823 166876 294473 941029 491387 311615 348376 579741 225058 808818 719447 655474 932566 973518 726689 181527 400377 680479 700440 576046 273254 721006 301609 274658 058044 778033 762178 888295 550924 086105 559721 690174 168539 948455 403608 882522 579701 682056 775105 031971 484490 661596 993551 048595 932626 151866 776656 892207 541608 791282 243630 856267 494017 165027 929358 445902 268907 850152 037708 369684 343995 600045 831132 084122 502342 526663 015980 438043 622297 312596 310589 341459 554115 078818 729129 941108 279539 231633 158753 807862 181362 343657 996545 178787 811117 194141 116710 922763 234877 847280 431022 998412 864499 985688 451499 952611 915964 741265 240704 238473 737814 129234 265116 256830 670898 570351 399673 090614 535591 036227 799225 160285 863663 581559 442351 452823 590593 963059 136778 761969 328404 287632 494658 608920 374329 318083 416646 714013 872612 188049 794950 221021 833748 408257 599730 851655 123341 741035 101779 328912 799488 355227 206264 154463 966318 021676 872191 151481 686360 013328 237416 513593 275160 541663 941862 705190 381556 691491 674584 685730 455769 697922 287189 689418 150033 220978 871548 501202 887991 169667 632976 114649 283864 735379 976485 264026 652825 045710 717701 322680 850433 090765 548074 573819 535414 714836 518381 355495 286340 820905 978146 517997 240508 723555 443881 523077 215579 591490 744782 414433 816299 162600 307397 354049 159404 715169 825326 585338 187402 756305 315524 555494 145761 986403 308807 936200 109584 530602 722411 643751 329917 370240 058286 013759 198398 929968 082362 617339 454276 516954 667403 340849 158316 955464 992123 321329 656588 582661 685099 905161 006531 064156 275574 021670 553976 674475 512203 015557 921769 517321 145188 589451 224279 048688 148962 616245 423068 511906 391401 743524 871477 766737 958231 920385 426582 391599 810661 290875 923833 504617 356599 654585 449836 832640 231955 742442 806576 748743 488770 714559 608198 716702 571885 847894 027823 403508 564845 785745 241330 638707 841575 092773 022998 002626 680524 071917 582243 691807 782914 331441 700890 622408 125447 971181 479273 600740 382667 878341 629325 416536 732842 120841 341006 138407 566120 057190 996664 170202 362665 912545 562360 232390 962050 965066 896677 958123 755884 244671 577048 892159 492281 950457 619984 491556 512647 025914 181729 978904 331583 407432 898853 859802 778569 579445 037628 403752 851421 605602 081046 617716 887406 807436 273636 000534 548323 328756 952975 672303 329221 734991 391208 183139 069762 444404 962318 189700 090216 285501 901798 218601 632950 806289 575393 614621 533075 640696 951852 038802 435034 290086 357729 749417 949341 815095 758978 609867 691459 712347 390091 269484 461496 156606 798538 192820 610563 904676 506156 498665 373879 844991 738186 121143 229251 547637 473429 195611 677391 947635 416348 538175 383841 168796 310398 343334 935686 340001 421727 560995 732914 062324 004371 486757 708676 447905 170496 614695 973802 124638 513854 407690 878242 137273 873057 144950 882177 705245 770596 374294 478538 835121 597506 826645 280984 255010 719144 393633 888823 510450 162252 800434 732406 462097 181488 849202 446831 474356 686293 624565 581656 512245 503134 237137 293789 190867 707367 184736 687267 145993 109221 876937 639805 730153 318169 561770 211775 323081 353228 966042 864823 208374 739194 681074 035346 036444 159406 860349 929173 371661 438367 109549 259841 087914 043828 096822 436492 635683 543124 905397 431730 199652 492961 328552 545101 641933 659134 216037 559743 736804 265391 624379 638800 240720 654161 326452 096419 516644 733836 128366 706864 005318 269725 827712 237266 265851 448240 829908 376846 249969 893619 073590 438538 477811 054906 164919 157178 996745 618784 254519 530890 198335 732722 726922 938781 489136 230544 235391 074777 532012 636086 799890 907136 / 3121 > 323169 [i]
- extracting embedded OOA [i] would yield OOA(323169, 1586, S32, 2, 3120), but