Best Known (68, 68+∞, s)-Nets in Base 32
(68, 68+∞, 120)-Net over F32 — Constructive and digital
Digital (68, m, 120)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (68, 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
(68, 68+∞, 325)-Net over F32 — Digital
Digital (68, m, 325)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (68, 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
(68, 68+∞, 2176)-Net in Base 32 — Upper bound on s
There is no (68, m, 2177)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (68, 4351, 2177)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(324351, 2177, S32, 2, 4283), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 148721 409545 217452 927122 779420 105333 482609 370362 913820 933711 700528 262537 048364 420118 804738 477315 419045 331743 132604 166266 592196 796287 417114 936066 576791 968629 860469 932080 649003 320626 239441 057563 546165 188834 648205 144294 891996 584261 956316 884746 763980 366884 557097 981829 271873 142552 747130 359815 328373 663892 755837 170639 562367 560742 465112 281084 163589 189083 431298 389673 873138 262278 492629 521713 315989 265182 358530 062120 170187 868423 375840 601359 712271 780272 281507 488320 501813 007548 690805 071418 536424 290581 200647 107865 149353 970342 204374 530812 395145 829403 633169 127694 035143 212839 329497 078833 572918 479277 347454 675257 078368 285632 642978 850787 117407 389603 163945 864422 656616 922680 566049 403546 310922 771502 217887 658592 140892 835026 259254 558378 267011 370361 113423 084626 317697 009075 628606 045764 834574 742323 595436 257076 300121 294542 848229 543931 966816 862124 825359 854648 598675 713467 476599 752020 762833 981248 155715 513721 246386 372420 886953 657935 641823 656357 061580 806688 655969 888487 381682 335003 851293 579117 552241 250727 317547 804291 882991 275886 131597 709645 459981 206159 632797 762452 007352 511660 582278 840541 764388 165935 897937 648318 815124 092947 435021 513924 899026 167324 621120 486783 515943 110297 850821 290433 146926 030995 525841 709356 944516 246199 027676 050510 643006 808184 367111 523708 379755 290270 764992 672793 551289 581432 142913 156482 591906 912788 228346 630352 269223 323910 601678 446746 465926 761192 697045 494045 694387 751571 524063 147268 400661 736275 261959 302989 827439 570798 043980 368962 026838 492570 540471 037269 854805 233027 187273 370931 316878 087474 377963 827000 902765 277762 307491 107818 570655 901928 257139 181676 942568 932650 009315 990347 229111 770649 131111 510082 123911 939337 582684 575442 228062 863238 198893 080581 087208 668809 848375 803392 516766 236605 658148 311942 139769 837740 027127 199570 341124 374671 421846 047300 115358 491906 999358 224742 753172 857234 067746 612294 844933 328821 162022 827499 238530 603242 904869 196865 788750 590401 952280 518271 397523 053651 225552 206234 007785 243163 700003 495596 352948 935074 823670 579089 130383 861365 662298 151743 847211 018362 855555 656587 506714 727479 473079 916946 637874 886234 832873 550459 189317 801865 483309 057762 951589 376936 325692 390955 231745 017495 632966 524436 697579 233005 569774 768690 528018 735712 857845 775655 373406 412756 850723 531870 879955 580966 399490 244128 112650 331474 287351 921661 637871 017495 226259 680582 626558 933489 447789 946104 668320 981215 884588 329381 378102 147855 776684 945301 891283 716582 955032 155365 767499 776396 798363 855124 895771 327345 894729 521556 039812 390554 169751 762644 808813 063812 543887 253904 535973 763944 319897 014743 985879 669340 582655 612119 828437 052686 549618 182819 295520 159495 168656 735295 391826 209167 090536 888961 002148 186090 100404 889858 334611 403708 354586 433557 611967 955985 415238 638684 865693 640060 344076 339714 762217 049144 293471 479863 572229 032908 503198 619837 913872 830096 868369 229299 282572 946059 806578 285221 050636 221477 630547 620311 296244 850339 061661 828540 444800 457391 750179 568621 740191 478059 641144 875857 419714 960186 396953 764930 698543 659106 366459 282153 092579 788007 699758 197947 575146 814502 524512 177945 423374 772994 946213 798383 286805 310434 060174 279052 852547 311721 899399 161106 860249 365048 890853 229010 984557 763545 265564 372748 535787 433480 236933 993676 307734 808455 784236 476486 508059 497582 759944 288756 824862 699462 144297 461423 698465 514899 929491 559303 970441 005621 427339 593247 532905 250300 223193 511326 757643 474095 813237 965267 917832 334747 716913 980285 593264 424836 211716 297622 234595 411685 950364 737357 759768 159253 913173 710678 289776 146612 214701 825799 992057 487456 920723 042855 975089 002578 995199 733919 301373 993132 698787 168559 178104 378052 692281 093292 897346 741518 666610 295117 553998 827253 875620 072980 237367 640415 214153 589026 244495 124641 202094 950940 500052 543412 230381 788757 474000 511510 296093 701559 176934 370139 424277 764374 177085 964324 013714 885722 023104 858825 157613 024030 306932 086745 640505 255328 013592 781426 092978 715472 897989 164333 429857 219127 371976 221684 406200 344611 110827 291607 773996 600375 141582 585917 081536 961925 627076 846186 213385 070152 476411 788593 315222 960540 975780 114452 383153 252195 164025 713184 840722 804325 542786 737679 344147 199901 050052 591522 044523 446461 053306 717907 006678 491204 254248 400746 298112 557067 541391 973231 731747 724858 057933 797188 671743 073062 198168 570952 508791 025649 863556 627791 311886 066822 771932 665629 562988 975246 683299 700398 274728 234826 200791 147640 191962 193797 913378 065322 571205 676755 563264 134352 648517 052904 769793 341487 452397 021164 108344 301618 041436 394480 619921 368688 964618 454209 825922 370415 278752 325505 433354 218181 014976 258421 926300 602903 147244 381164 104118 559263 311576 518293 138442 721550 678531 526594 081040 598529 224820 937841 690932 730226 195996 586607 529132 755685 578139 089280 396783 299104 302650 025504 388845 650707 432432 397936 063081 068374 972016 608849 235749 663808 994422 668753 072306 809486 125428 058167 918460 992390 115366 672659 347974 268984 912597 291471 305386 012282 835287 973244 612481 003430 782759 446045 938989 252959 908748 027283 268447 721164 828815 013466 500599 914883 801461 445640 458018 468176 563654 723734 883177 190023 008475 008050 537931 722941 545841 212700 950398 216652 409484 605468 053808 649177 554819 505614 091443 500339 284718 029501 935878 301787 205146 104355 114147 782381 801276 686334 650270 228448 000338 675947 994524 687174 631464 849700 483400 665402 585051 365470 673626 319759 763766 357800 513710 970643 127640 107141 496127 763910 916560 688611 260942 350678 857627 445097 942512 115656 431849 835359 683491 079981 274043 844790 533786 768016 231837 425692 614465 188318 093757 974383 293636 630029 657993 865597 183506 348716 570852 899362 632997 736968 253121 362518 130748 622425 698035 346749 050899 925672 194482 665296 782493 592753 748654 225645 854669 792159 192569 001441 989471 446835 597983 532394 608359 219722 169873 859310 102905 840103 291521 136942 633015 904960 307545 680417 728633 526258 386377 646980 856545 354957 209624 174754 412218 063382 455476 959490 016294 049064 564572 195430 972684 586828 367076 467984 593411 901272 818600 084241 202713 843130 400729 772088 796079 176812 862272 577692 851228 118158 739788 120667 690657 698425 158804 667216 234320 024615 134873 843840 646534 803350 658893 886924 795640 777534 328134 592722 361075 880462 120361 467160 223539 090677 414231 696606 960271 606429 949678 773925 259074 565600 803203 512319 127337 233698 974282 060742 238162 077898 350729 528462 993891 040658 344272 399464 793916 546736 171579 395969 729791 989061 658041 330875 550396 503598 518139 196554 953433 608615 192200 426678 990000 596622 294191 821093 427041 793409 612668 507064 044949 405122 474502 280859 816725 444016 525846 896422 884193 283820 714235 842557 569047 132184 162660 667872 771938 510769 728777 895420 754467 569375 480086 815381 384794 850911 547432 965949 236568 536449 737994 305924 546482 233113 360085 790569 824176 653332 295070 874843 928058 520138 070557 416035 712070 483483 042246 841210 166074 701524 010466 440523 806081 508971 410934 899271 855567 518872 219756 518845 226977 954457 224526 694885 931184 789649 206270 837326 603838 554112 / 153 > 324351 [i]
- extracting embedded OOA [i] would yield OOA(324351, 2177, S32, 2, 4283), but