Best Known (7, ∞, s)-Nets in Base 256
(7, ∞, 264)-Net over F256 — Constructive and digital
Digital (7, m, 264)-net over F256 for arbitrarily large m, using
- net from sequence [i] based on digital (7, 263)-sequence over F256, using
(7, ∞, 321)-Net over F256 — Digital
Digital (7, m, 321)-net over F256 for arbitrarily large m, using
- net from sequence [i] based on digital (7, 320)-sequence over F256, using
- t-expansion [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- t-expansion [i] based on digital (2, 320)-sequence over F256, using
(7, ∞, 2056)-Net in Base 256 — Upper bound on s
There is no (7, m, 2057)-net in base 256 for arbitrarily large m, because
- m-reduction [i] would yield (7, 2055, 2057)-net in base 256, but
- extracting embedded OOA [i] would yield OA(2562055, 2057, S256, 2048), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 65 840017 233859 853956 259638 474148 383572 024850 611760 845880 616489 835000 836054 173017 675977 639206 005656 105111 271828 591264 650768 697826 993968 189099 231840 924529 041194 420093 249845 968752 725584 970710 871524 338457 397587 600477 878573 481747 173479 632223 415588 784649 040972 615107 270993 198637 662948 253005 716017 364613 799101 605185 482520 506036 571026 954680 048578 384682 235642 379639 065881 722692 907599 671048 401548 517607 520881 885559 449658 387800 270652 049173 527824 125653 957766 712778 581314 844045 913362 964117 647145 351380 420885 358120 925683 131798 264475 698855 361808 601824 845143 266891 169693 426366 562914 743906 892360 619071 333409 579702 598628 597627 251392 019010 096229 127459 264230 830578 856488 319769 458089 583669 596001 505152 309717 238189 629112 720918 977901 582656 641587 688785 498127 384969 633766 369925 426434 150452 243259 547687 484778 896503 537563 818942 585444 951842 267314 363557 169071 203269 903112 751128 390539 649922 825411 015253 318065 633361 832766 093118 678591 039210 073761 947193 414964 189514 312066 422946 122652 501857 179549 222426 294609 791916 621532 574606 988471 039870 782699 909937 570505 887307 052662 253128 588009 310659 560935 541878 984650 167406 756721 464403 469978 389298 090243 289933 122984 181066 351715 597339 308331 626882 847379 488816 595057 423897 980697 437642 555723 066476 877278 193779 883239 615684 576091 294491 520351 549499 918093 626228 649487 727020 470568 445749 723527 028881 240528 386716 270534 112658 220098 062869 263467 926948 147026 266715 444590 689784 841308 308823 624162 426092 726027 703291 250333 345285 925614 183612 832650 182564 024843 154159 979638 286457 686922 475459 154641 747010 447642 212768 370019 871029 986707 611951 112127 851582 023251 541289 759223 217480 273711 565587 832537 427409 453176 266016 531754 463241 646334 267527 190179 622654 865612 720779 594941 423169 038202 047374 159814 161197 529730 120690 220183 212053 360889 632847 041323 835588 758792 280112 665141 369384 481971 650881 308531 435403 905992 958974 218408 234860 605920 888408 141928 154591 350831 199880 295655 688104 552530 427905 605876 626109 224271 863322 705718 542192 521842 966025 339704 238675 584359 201493 833242 052352 907933 702765 578608 923943 858799 152818 796265 957111 820008 886177 060537 782246 042085 746168 768560 334123 056771 417408 377753 267116 575188 671269 812272 751621 059825 521883 893043 040833 144621 022863 414444 171668 906567 964898 614254 514979 982404 202630 036932 717004 956948 860437 073793 928994 543551 634316 770995 342641 986130 689489 762405 223385 830489 198216 011740 811176 989105 901892 695729 199924 546983 538664 817630 040301 932753 423508 559513 446022 844066 602883 010857 243291 918134 806847 687927 194263 746875 601434 752516 985873 148493 067228 692362 610926 371775 444038 102237 395834 101414 208064 635103 672501 411950 220082 172190 783594 527772 021458 517894 572513 880772 455723 605724 774819 632736 461819 341680 216797 930748 963279 571558 072087 020251 984986 862703 196841 647530 694069 360880 168969 531205 590197 656616 304970 028989 070176 038561 803025 091136 350255 194728 361409 830204 556874 621360 475565 004449 119305 776698 020120 487963 286870 596609 866499 370918 202118 109255 854033 885845 935846 916903 651280 595781 708100 316425 675368 975958 040463 235588 032477 225186 653469 394603 692350 202582 460486 434087 096888 138865 842642 167543 493493 834406 731955 131482 189332 983949 415134 435094 837592 423211 151674 939479 223147 569875 889895 728033 975675 521222 647974 808526 143191 182867 155918 369243 018858 774829 315090 884285 105540 969482 883568 330975 371002 285316 757328 447694 134821 710827 404850 700885 257392 051715 368114 070336 425368 874732 294134 174788 469945 048167 396024 221665 704471 779417 616519 474273 172986 342781 841544 905405 972583 599293 987523 011557 396018 552456 798586 406323 697407 089846 918650 363471 146597 707964 024511 136853 681039 493470 728910 478452 141044 149659 568661 778990 970575 679945 572160 527548 942419 893928 941106 926983 426375 969988 430661 139100 957752 297959 539228 487963 433383 537565 523338 912006 639029 456841 328609 067134 370735 666267 835210 112850 284638 842662 293382 170869 818927 177645 701114 895957 201237 363674 325477 821385 670683 661065 169057 325314 256876 857533 428414 189896 290416 897655 453167 851810 814115 117727 898761 806333 503643 119451 592383 691550 382841 399245 915138 648154 191413 569368 590573 338660 076612 572259 502824 417082 823482 315161 313414 645010 880130 938732 361583 302741 707102 429230 777602 227413 956348 073535 455122 655853 460026 702831 365581 533468 495492 106083 994128 226280 004284 636388 916391 885757 425500 009271 814218 758080 747219 987410 060559 990345 599601 769297 305129 567015 622620 404715 374732 234134 386209 736348 095351 112841 975587 203746 788644 519607 896411 823748 478934 374832 676159 944757 324824 552398 037972 305963 128363 547665 074977 368213 469114 322224 950190 020582 112118 431978 705858 789762 818595 174298 524685 460588 048653 134664 015139 869223 001571 621856 757379 742394 664055 608849 296276 213259 436968 647684 947305 310787 992914 490950 079587 061200 736222 923999 719050 749008 954222 935352 596834 047186 055950 882798 181368 150799 511507 400512 688240 343117 489078 021320 499070 009449 258724 054813 742379 030563 855417 654408 632439 901932 730487 168893 533606 769851 369853 466656 879414 071699 379702 422145 957069 039686 099488 908073 225259 225057 159616 559552 426371 028559 948919 253491 383742 534297 371044 493532 588341 313345 878576 782621 617691 719629 554368 326883 460851 964315 368133 930661 118442 519635 217634 970275 824859 003783 239916 435455 996123 517674 323968 / 683 > 2562055 [i]
- extracting embedded OOA [i] would yield OA(2562055, 2057, S256, 2048), but