Best Known (29, ∞, s)-Nets in Base 32
(29, ∞, 120)-Net over F32 — Constructive and digital
Digital (29, m, 120)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (29, 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
(29, ∞, 257)-Net over F32 — Digital
Digital (29, m, 257)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (29, 256)-sequence over F32, using
- t-expansion [i] based on digital (28, 256)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 28 and N(F) ≥ 257, using
- t-expansion [i] based on digital (28, 256)-sequence over F32, using
(29, ∞, 963)-Net in Base 32 — Upper bound on s
There is no (29, m, 964)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (29, 1925, 964)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(321925, 964, S32, 2, 1896), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 564 114362 145765 078235 139794 256287 925189 697613 689716 917567 177254 443175 641915 495455 816094 224232 276858 943369 165060 629457 901704 513946 680068 083633 184559 263811 657910 393690 462688 015742 119294 561543 498209 972562 462704 203113 764378 806801 880631 411710 339913 572139 394898 647993 443872 893197 789988 642649 527773 980011 858726 303913 355991 921331 451724 569757 450968 570505 442000 329634 723612 805170 911824 070466 911098 431513 417818 712255 323230 558409 058657 144790 793479 199794 228912 261078 347301 470507 142438 688081 895233 170568 999511 689470 238321 383151 130574 205418 235080 516311 458264 069274 080321 812821 071832 203185 056051 028858 338225 536988 193047 657962 713080 524292 599061 454282 799648 561630 757083 598450 044557 968688 408640 418179 454094 540535 469008 145730 230348 514380 384702 350970 238352 616520 009852 213815 011524 947216 568036 172043 177429 169379 653962 555350 696680 293229 396455 854688 016788 119212 961132 250655 724700 950629 715458 865012 626459 464646 860436 603854 855042 514774 497327 973454 777280 379020 580064 915948 234876 255107 194810 822911 739042 123482 472816 763454 245190 530565 230212 121051 218955 083507 726765 493415 658426 319887 031281 997819 049408 334043 161650 101516 947539 454556 758644 274689 589212 903860 416070 460701 775710 899710 687435 275619 658021 108374 987745 455315 312331 923026 561163 430905 524844 146394 887273 089186 893035 729634 493800 783019 586209 905165 934560 481056 510312 763815 325019 703662 156008 220710 523892 629318 337527 317720 206705 452467 097811 612326 872914 469759 554601 442967 450001 663794 697100 992480 456096 636409 883871 365448 395250 674044 039600 447187 336509 330561 866204 425934 040957 416488 188742 723212 895402 192142 841217 492706 903394 670042 559594 754574 908925 276289 418466 288032 054157 058574 152368 196027 985210 562655 238680 453402 600157 050774 375908 638954 751044 452553 182130 555875 985058 956476 872043 421431 585570 139447 724185 384541 704597 025218 778905 032248 190839 822938 708078 446298 434463 428490 969334 267007 267140 462184 465775 597266 886417 180896 920944 603581 210656 812852 180130 453772 305134 419864 543425 557116 961603 836909 924448 646102 970457 519385 786501 700277 242260 816905 173264 090386 892788 296019 159168 104636 834048 369661 360446 393004 085017 717256 332472 689096 135025 379808 349503 491623 241307 859517 029353 249843 806337 149464 966349 577827 668583 045961 356617 016930 026268 663116 723510 021949 748419 251873 422062 967346 759302 642207 682749 890155 515922 668480 093056 859546 041728 947826 989059 792703 705650 472949 992920 416736 161985 912549 395538 349836 592720 254124 583933 090305 234282 739811 394773 204055 523331 267218 167015 478099 788807 058802 029174 198073 399282 589707 718828 895099 548834 891248 303474 996900 758452 551089 862101 882452 131805 912246 511910 408237 143634 439345 402635 640374 263143 636198 548490 641490 985803 260779 892734 120441 161155 007664 864521 066128 890380 252626 815396 986567 821704 018966 343904 049846 718463 538501 626736 215955 425497 319892 832493 075546 173473 196316 494586 651483 227637 214088 776234 322098 396862 059078 852387 687518 919066 795518 400433 964728 767612 572030 135063 876248 063370 735305 516483 182720 063833 438682 369245 669317 989105 114837 537272 988794 131840 000590 433885 356032 / 1897 > 321925 [i]
- extracting embedded OOA [i] would yield OOA(321925, 964, S32, 2, 1896), but