Best Known (33, ∞, s)-Nets in Base 32
(33, ∞, 120)-Net over F32 — Constructive and digital
Digital (33, m, 120)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (33, 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
(33, ∞, 273)-Net over F32 — Digital
Digital (33, m, 273)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (33, 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
(33, ∞, 1088)-Net in Base 32 — Upper bound on s
There is no (33, m, 1089)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (33, 2175, 1089)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(322175, 1089, S32, 2, 2142), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 15 599998 564163 540469 564391 078095 371419 390889 467471 086381 467820 180731 123140 903588 469341 075917 918324 746317 487789 785250 467760 624318 967580 141944 567290 134222 077130 375710 676792 251469 717760 034510 837733 391441 947683 255438 820122 297056 862671 992377 701951 410516 064559 213995 281565 789804 116545 270853 992304 421738 408588 575277 135378 946752 950369 664586 153476 085319 831419 100307 436281 504033 565502 231333 339795 727704 332638 258124 856433 427839 866880 962089 722175 484267 777535 816304 492959 486473 216217 302637 467653 390158 560720 070601 734498 300709 544748 590732 061890 346333 685326 434535 560465 477050 653280 652256 930077 984850 065716 772165 038573 894739 549963 428646 691219 066750 714128 858250 818926 925546 552332 922244 056715 710706 890594 840047 250010 649704 941684 984617 136169 514962 507981 710032 886705 003173 839041 076624 580903 113515 721280 912838 940771 752481 507642 696690 223131 081476 079903 560643 398013 454008 044442 165147 032019 042135 658453 579249 864591 073331 827750 907161 988224 209038 359949 318500 530493 429073 464670 983963 290469 900084 278605 571508 335237 520247 167391 278369 562529 316217 817517 506442 366796 887234 825399 578250 583491 425515 178302 184476 932129 494358 704229 139619 393129 185778 359772 901931 464797 407267 767284 309554 840513 840640 649778 029906 964739 187884 335962 078166 083884 924496 259197 073217 721783 121734 179876 660637 237759 302824 840337 015668 920981 196011 426088 330546 474089 351480 859595 116014 025897 144556 304843 599153 292870 964392 743682 369074 588596 011949 340575 048612 640226 090455 736475 873735 375322 292413 719566 193405 814244 902230 410948 687644 957774 935293 322357 256107 901167 190120 276374 862095 723104 874077 227695 192361 841607 196816 546080 119756 139235 196833 059770 393547 370636 548328 112159 443626 590105 845091 293771 669669 325578 860632 942176 475537 527151 881383 032883 110350 207310 108427 345529 627716 506588 272770 003327 323154 760832 328811 427390 098956 000850 059476 388091 118522 770197 832443 520980 886247 680269 127137 037663 733527 496311 853291 235320 739256 577864 634632 360076 734583 726826 430000 037559 830527 345409 883265 919516 687967 851642 276967 061018 871879 094708 194027 096675 048990 045379 617983 526072 487503 118850 171482 434614 566401 270045 671127 190834 618890 991786 620611 094004 747615 366980 662751 097951 126652 963915 447439 721590 161689 977626 041362 239212 209888 006705 009987 411169 877161 479084 928594 741317 054444 784588 881961 147126 675169 003071 687176 121168 587658 984651 893036 337993 556197 737911 743578 449599 147374 500598 840579 019264 577453 538535 597240 261333 743302 033150 374516 981447 506967 991595 887663 886854 982754 323741 999905 439786 866648 053482 495687 890133 045654 606047 306066 783033 134706 114840 389205 936347 726555 969242 280711 936560 941839 135974 253890 941793 541806 659730 466599 784422 970319 621370 190335 927105 425038 071937 970529 778487 474957 882275 091071 758495 186547 183203 769549 648679 037299 421028 897419 160873 249161 571479 577492 881540 149000 261252 226016 898263 975679 366129 679202 924793 836675 918544 830651 343790 239521 609187 992930 487932 992692 329413 030691 096879 807686 538204 333445 883834 008735 202386 845448 405293 568658 540767 070836 845601 330224 198596 597743 380700 952265 300447 653575 793149 297014 457860 020571 952193 332651 649362 493100 002181 085176 129189 475289 362336 800415 102222 305241 811082 224518 735805 533643 055562 177130 340739 095328 819647 573451 800287 166528 753734 955495 195902 432744 415907 589840 257936 736705 900509 497592 684918 965227 659468 905163 076517 028988 913369 308615 309659 890676 564203 859605 410285 318867 082639 904968 214872 878574 709024 581351 017400 450596 995072 / 2143 > 322175 [i]
- extracting embedded OOA [i] would yield OOA(322175, 1089, S32, 2, 2142), but