Best Known (39, 39+∞, s)-Nets in Base 32
(39, 39+∞, 120)-Net over F32 — Constructive and digital
Digital (39, m, 120)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (39, 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
(39, 39+∞, 291)-Net over F32 — Digital
Digital (39, m, 291)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (39, 290)-sequence over F32, using
- t-expansion [i] based on digital (38, 290)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 38 and N(F) ≥ 291, using
- t-expansion [i] based on digital (38, 290)-sequence over F32, using
(39, 39+∞, 1274)-Net in Base 32 — Upper bound on s
There is no (39, m, 1275)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (39, 2547, 1275)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(322547, 1275, S32, 2, 2508), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 92 734812 698316 106985 435894 688454 173281 488849 178851 439276 026349 735575 358487 507039 386630 837784 067489 612416 185985 040354 679139 819583 103406 446800 294150 929137 988616 631726 344011 027455 203153 027821 595651 742719 952377 204266 557700 184455 488344 730769 005623 864127 421998 622635 775227 384124 754702 182028 608437 839533 272433 794793 864605 454590 311454 075489 613661 303053 213377 444687 386652 434183 381801 941079 128995 946890 010724 696782 931546 706581 888955 015019 052190 812443 978726 373189 269031 319556 592015 973716 146827 646779 427239 528111 783792 880574 553295 224626 392605 779664 880071 866101 223542 899632 703801 001147 244894 214933 774040 519554 796865 557574 792483 310779 261584 529538 936595 810081 967766 842350 412271 416154 672461 510499 163299 046590 211483 425584 115832 797164 483458 618530 403021 707556 268314 286531 987698 966088 116016 684200 125737 991029 790747 820275 834582 900253 496298 709223 921767 384190 607796 066771 077164 008218 928151 217488 624587 923452 149876 005708 044060 724814 720696 360964 286265 127173 839497 705729 689585 797932 561992 968032 617660 015433 962122 169000 815721 376381 918770 882306 293810 450673 812452 453024 198742 395517 379767 154948 370362 430037 419922 815986 564208 477364 151664 335103 088904 165631 860673 006971 447877 446806 739778 043502 967676 106644 575345 738582 472145 603486 969566 022035 931733 987951 654100 488523 144835 431222 113097 450711 890326 514860 722913 868658 703697 712265 210834 222189 025203 063028 230526 426563 867018 887772 725200 063781 813795 224071 898638 782907 918723 683734 129526 524000 412720 955903 744036 666941 414382 529244 942740 870530 786012 686581 345353 332620 886932 744066 678011 338774 902801 355205 751584 420404 239104 090957 055400 589238 034637 729465 556565 505120 306813 133883 880181 859000 638944 239388 281432 154887 682482 036680 426921 510784 498178 373665 442085 680862 771329 039111 317982 988918 250406 920033 779936 190088 866207 260156 372892 784468 206218 345445 882855 962437 599508 518764 412766 262489 689544 237326 660370 841586 244633 003642 303798 161284 254777 912564 271907 756352 426861 561529 322317 754178 697560 880952 937641 580424 350988 264389 816117 265108 326453 451808 030564 665282 079283 536870 305195 190596 388381 546587 452222 402081 421140 843733 377255 170763 811394 092784 555623 441375 152820 930365 823024 820710 966287 023182 791775 975606 495756 136612 634725 517386 779407 523841 727206 528238 575603 750059 769733 733882 407069 709190 260387 114911 829381 764940 015536 511800 531555 759789 230094 339189 915610 941262 421795 532199 951449 002721 841180 147349 228022 866199 062282 822565 078516 447027 401248 644761 100769 953620 018269 593507 512455 628102 692855 627783 902842 280040 575585 261149 171446 020293 106896 091768 770621 702604 635752 427784 564703 210458 765413 485308 865980 698930 521299 262529 083241 018447 494603 523086 666769 545488 100481 524953 660022 110698 250951 950519 983532 616078 501374 693896 999048 135657 256962 892750 644260 216269 567434 436578 421497 805548 912931 140140 293126 456204 171097 043662 019238 017916 704233 033729 972516 357153 004640 503946 460114 849750 659164 535044 725788 948166 125564 891966 599415 660948 866259 202926 278137 960914 169440 261097 353367 172009 516667 020986 611079 339193 737130 082462 995662 196273 412873 806774 269035 517827 377755 758786 700104 332483 058425 776531 984356 740802 400029 621276 952990 155421 703944 311219 352096 269708 420759 321234 588278 632775 164427 461068 577435 480327 429955 414881 670461 811596 578225 101026 034302 742901 989434 942642 419816 756492 687901 829521 173936 324352 642923 551087 863998 947479 732090 712554 446013 943420 314784 413851 822236 233222 723397 605732 202534 232604 969633 720467 613045 180903 345609 162475 359524 681453 154938 864400 947307 940310 327721 172724 187978 347147 895763 081980 231327 152651 013844 518757 788193 978502 297652 821852 710284 601273 882075 784987 701771 872036 708181 608111 583201 829418 229096 815714 307271 700107 125616 855432 789284 652485 359563 001406 296144 875106 333767 959660 763805 205952 449823 315915 603067 242657 861034 847403 893960 411689 036339 744393 731569 125612 226365 531843 107698 687696 009540 065526 686583 401960 058314 530842 455202 409508 981012 912215 785487 533252 450759 309480 178373 191889 233716 934208 551906 739327 914847 666592 496800 074956 192242 753301 102232 338432 / 193 > 322547 [i]
- extracting embedded OOA [i] would yield OOA(322547, 1275, S32, 2, 2508), but