Best Known (37, ∞, s)-Nets in Base 32
(37, ∞, 120)-Net over F32 — Constructive and digital
Digital (37, m, 120)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (37, 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
(37, ∞, 273)-Net over F32 — Digital
Digital (37, m, 273)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (37, 272)-sequence over F32, using
- t-expansion [i] based on digital (30, 272)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 30 and N(F) ≥ 273, using
- t-expansion [i] based on digital (30, 272)-sequence over F32, using
(37, ∞, 1212)-Net in Base 32 — Upper bound on s
There is no (37, m, 1213)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (37, 2423, 1213)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(322423, 1213, S32, 2, 2386), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 9 134161 839141 866588 401270 624153 824110 427056 069870 141505 770699 189536 714949 953226 386337 194146 653706 535686 906594 152338 389487 747169 299075 832713 257483 079595 792322 612279 577229 517907 047323 698978 107498 212730 118624 368788 079343 491195 939521 059279 904096 057344 019100 502187 877932 107070 754784 060102 176859 617358 607684 121962 568002 556173 735982 469342 694815 449717 635361 788052 380567 813529 619921 364646 037177 479077 247295 272233 880373 446139 073642 985639 775316 585728 602440 931914 839637 257464 993230 190808 950894 719096 160125 607357 653185 100523 702023 378049 142239 198138 369708 663765 754258 962340 668956 955227 093335 039100 547036 922886 933685 813176 571035 006286 252092 395662 681131 675776 166073 365677 071858 984312 494187 347127 815298 779364 215727 849918 368058 233218 625966 041781 233635 090735 749485 139200 983190 580048 550304 937625 338660 218142 308060 188961 792093 553390 581185 721299 833482 679611 242977 482524 067153 346957 181104 922662 453543 685427 825813 673481 757701 227146 478622 452524 813509 160704 324961 193308 951445 453299 017907 807185 864791 814963 946643 695963 044792 066923 351423 730294 115414 960830 305213 294277 790418 919359 598271 905006 535045 920825 473144 734700 292829 203573 420476 640625 461135 317349 254166 080953 114080 352805 196486 048626 437107 930835 041570 395922 631682 881463 114402 663720 341493 407461 908697 694582 275323 055222 843593 388915 659060 604668 413457 615716 287859 086774 760637 875111 877315 987073 850451 651637 607940 236761 177897 580429 405303 360096 363800 156178 383465 395813 566090 824211 575300 633849 892096 415575 246544 790712 584390 342334 509595 164922 010215 405550 618704 449930 826238 071674 376874 625583 589121 256410 033861 939443 235949 205391 114023 912190 125425 995050 451560 232843 881504 568137 347654 376161 922774 632054 404137 812741 605444 837545 544508 569245 470006 597942 741300 349697 598444 099075 793547 471103 605041 236069 281938 645438 230443 113083 390698 434221 230616 994935 901809 410677 998130 597982 085451 819067 876110 538409 953266 789583 867860 641979 250072 158606 781139 881706 555194 984020 390568 696195 913898 294529 402153 707492 573643 186535 719409 648949 850042 815214 198525 104505 929582 477066 416818 161449 855239 830695 914001 757341 046574 047420 073003 313474 874467 176386 820351 798650 485576 302845 963342 547423 943435 297035 540759 130176 975409 313971 571087 149285 298382 967860 498177 068000 153662 265057 339569 658017 018017 012582 218152 381542 634512 295492 731278 963003 097101 531402 273363 075750 789200 348761 028708 653176 396337 388931 466738 187652 507077 661706 226135 916975 547418 430810 933031 411238 563415 227337 196176 472313 044293 165738 490981 444087 744032 954318 431196 902719 443606 903143 636414 668101 151132 754325 883449 688561 733479 810852 219926 510174 290544 380811 392937 567460 718700 190704 633682 857285 970669 743105 555032 222177 501760 989425 890094 376035 388360 727908 152345 190073 662221 667219 084987 198454 277606 659309 047120 627416 652031 952839 437768 680294 835223 876717 052108 008167 714433 961866 140044 216353 029581 173452 437475 660889 812113 227634 153053 848318 322863 359513 529793 054540 187755 806712 351137 419150 416679 954552 290222 171756 698048 526228 194672 432126 941460 220907 181484 378924 258171 182131 669929 358512 131386 919241 982535 858639 628105 316611 979278 479301 966376 918810 502214 848856 590471 176353 584058 881011 153194 122266 717449 575940 433210 099029 204851 312018 996503 384117 982801 240997 964549 775380 749176 941477 096220 369971 022292 221657 815946 247843 791430 252723 694416 427786 240077 069227 944414 406165 509212 684261 770439 662946 009388 857389 117364 182867 758218 629842 218476 895487 993506 124418 742807 461827 158464 468617 059029 697938 462982 314098 514817 402888 338788 464478 841147 823269 208103 231683 229972 458474 833967 738364 724045 808723 529192 730285 345057 833487 398801 336268 287936 759226 157630 260216 934657 268754 844206 739650 393673 404693 868946 539265 451002 961432 013587 340895 121104 967302 505398 982917 831490 142185 671111 338088 958572 019519 402487 670769 849468 571447 484423 403939 125667 221867 593728 / 77 > 322423 [i]
- extracting embedded OOA [i] would yield OOA(322423, 1213, S32, 2, 2386), but