Best Known (22, ∞, s)-Nets in Base 128
(22, ∞, 288)-Net over F128 — Constructive and digital
Digital (22, m, 288)-net over F128 for arbitrarily large m, using
- net from sequence [i] based on digital (22, 287)-sequence over F128, using
- t-expansion [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- t-expansion [i] based on digital (9, 287)-sequence over F128, using
(22, ∞, 386)-Net over F128 — Digital
Digital (22, m, 386)-net over F128 for arbitrarily large m, using
- net from sequence [i] based on digital (22, 385)-sequence over F128, using
- t-expansion [i] based on digital (15, 385)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 15 and N(F) ≥ 386, using
- t-expansion [i] based on digital (15, 385)-sequence over F128, using
(22, ∞, 2967)-Net in Base 128 — Upper bound on s
There is no (22, m, 2968)-net in base 128 for arbitrarily large m, because
- m-reduction [i] would yield (22, 2966, 2968)-net in base 128, but
- extracting embedded OOA [i] would yield OA(1282966, 2968, S128, 2944), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 29 661368 673552 928029 013561 888334 185451 636148 210549 222126 186351 987382 101448 476091 100010 238952 046168 798511 432227 232866 488812 511524 933495 499710 533017 633909 028115 372255 606235 343995 239316 807243 647645 402643 281569 876419 436018 014206 539868 499810 838715 746578 980567 106698 961278 012769 851004 492440 337630 754240 243406 315122 365309 702960 206048 360760 478013 444978 824806 002037 747105 918224 746730 175598 456918 354476 864564 396751 588033 040143 532214 051355 209454 957611 889478 502253 041026 317136 366762 230341 493153 107423 122827 203004 774474 456024 401466 467786 063743 003083 574051 881693 214437 596048 711828 268016 844494 682141 762437 447429 776546 510825 086976 375291 779190 015902 472286 660269 517214 133931 699658 539741 842458 844410 386318 744952 440978 940373 965853 544568 380358 923734 397393 184941 673964 091400 160096 060970 864626 851357 162101 134976 751170 645083 502681 879595 173796 493766 870353 903336 279928 510865 144313 472134 014055 696309 178554 168855 644782 253777 215280 203494 568276 039356 036145 316670 237736 279765 662180 645961 857768 816134 265097 108271 892655 288790 822976 584448 849024 345093 411119 991251 437383 376949 644403 520639 337473 384301 021004 217850 663115 378892 244850 266936 233437 906012 873490 434781 010815 273379 723262 724732 061187 839887 167567 020193 820087 091847 532072 274344 751662 790224 852651 456623 280147 958887 610135 737616 741729 793943 594488 867519 958161 762495 916505 224031 767719 706497 582516 841631 061621 335303 629669 967021 822675 624456 331880 627453 375911 056037 517018 253458 731599 541059 926228 912297 614599 569266 290377 999183 918370 765493 420093 410104 438184 143458 889768 894149 512820 975867 239996 226034 467527 651832 746171 079805 497856 315239 028837 170618 499603 932629 076844 115669 794420 281616 310361 842747 090737 408161 073926 786139 749417 793414 903987 475295 262397 043204 599879 089863 400842 796846 083912 292998 815969 460278 993671 120840 690221 580510 620148 738534 045854 630345 773790 943724 975231 148682 215096 629033 113611 074305 529044 458184 375746 917494 533122 146090 506313 345744 824553 530496 262231 839534 903760 385654 724805 185678 403563 827763 084409 368375 618512 346958 650353 970742 214796 110248 489003 398191 781496 024156 550760 473853 255524 806552 997607 278425 457184 660108 110055 137372 061677 169010 091217 659650 422272 333764 140190 834123 723218 655367 074094 992016 547469 257403 019625 589748 676891 048946 182718 054675 823945 614407 422157 656057 374097 788634 173687 990119 107303 767365 578139 814137 704775 771416 533557 248003 155067 978212 003800 163499 512993 373093 683452 951194 405513 839727 158954 886158 618857 872189 314180 588295 597609 378922 712795 117131 905748 033701 752364 171205 383639 366653 676919 901310 441362 624087 321253 223441 954908 737585 161619 349969 757092 177428 567055 552369 951481 096041 001687 753453 601785 477383 258971 475060 464612 264938 328814 378422 519599 632058 536653 636343 577779 296588 364238 561985 285648 079096 172849 086789 303436 318722 498522 989753 087665 456992 084602 288359 380859 124071 341381 650380 001046 144057 086989 283248 993398 864190 847772 317950 734181 156818 193381 714360 832768 454858 370223 307022 976943 241437 528131 240539 346741 410812 779948 051439 119517 795735 276546 292872 653830 767673 945539 111909 127269 882425 420147 009903 553381 623932 624120 437502 258734 297760 187120 909948 057659 509660 538736 734712 401591 544778 635031 055114 668195 391525 611453 810022 300622 328382 225050 149189 829511 309761 754117 503714 996932 976077 946434 708192 416873 283452 305179 526497 047419 316952 352765 057630 153666 152468 948769 217852 792948 472367 932791 643829 953328 987728 862968 386297 068404 218010 144113 680739 461248 154744 257164 044617 886152 242924 411172 459526 129287 442361 950820 072410 258704 598614 282340 237709 715476 971363 313968 866900 879875 304001 866164 529123 672881 150327 872746 008692 690471 039558 280633 375188 802167 888673 165446 601947 784298 297270 276875 169464 115939 839687 861967 764656 485425 649095 390562 284816 276574 533978 757355 507108 275637 558010 559017 109191 382651 461401 042074 641625 533361 659475 194986 817769 434009 156519 762946 239594 273743 840296 009200 413016 562913 202816 885213 269224 833237 278847 975369 053165 008148 613858 571544 846971 338851 309237 058992 583025 900715 092646 521022 606567 322268 455231 299136 769184 900921 048456 680780 982984 682201 121149 146954 247790 208281 164767 064514 801389 329051 990261 706123 512141 373224 688541 459737 749812 618554 685897 311672 578951 670153 327671 327565 898067 643594 550911 132245 081095 017836 233787 303836 547270 904119 637025 105755 275570 418780 695968 204328 868193 355921 256248 662777 699867 902039 311764 563504 473757 845004 385578 108323 654135 665451 411301 494418 479870 797204 782434 768417 149708 293205 949027 685615 880811 069693 937101 091204 361807 341599 777882 787512 031225 082085 368118 500998 870713 315321 261435 155662 521938 816707 375811 324949 926394 249670 691943 715274 983250 277654 784128 245115 706479 981621 852589 767892 388683 973027 867043 095966 989625 151955 039832 676609 031752 390670 216263 990512 322162 172493 916096 192566 687076 843642 419316 742671 366929 668414 606162 574878 862198 757894 651905 852333 641714 004793 409769 401154 679963 345303 688998 667059 205188 957581 947706 690828 084704 844203 275594 766032 778783 780906 823787 041875 995023 862523 411055 428942 936552 968368 484979 515318 331995 342751 547855 141587 592184 478112 676959 988463 374579 801309 792419 183407 406294 859995 981803 650001 280340 798986 314785 659927 812258 413927 052440 463504 998431 882669 186613 241491 383494 211702 460684 514437 412876 832152 657420 236551 651239 385612 448354 881736 559545 113028 372699 370213 221401 222426 178584 146851 271963 516083 662993 199264 006228 050833 164077 602647 167816 218752 031246 318365 145482 338457 004776 426796 160093 196367 711285 927601 626419 293700 332960 625937 563041 786032 464091 480681 036875 313980 797943 185475 484289 645836 604114 859518 449256 708549 776342 240712 540213 590634 407026 536626 737242 785903 727931 727273 985282 504109 570001 665787 333804 467006 855093 602321 995465 729656 448044 640931 877482 466566 680160 686962 198336 101767 038754 488225 759467 044133 301054 750148 779172 900529 978157 627851 830238 780250 057002 754852 167490 033937 905490 093890 165349 729077 215974 034921 993543 819504 725836 061441 274527 136424 134935 956283 566908 043685 643840 014038 347014 712771 562043 447604 338982 403807 232291 162532 032993 200583 046176 510338 166429 126217 619689 052804 956114 209902 017025 495773 517495 708101 290743 956498 180730 265461 565753 782892 702142 124848 096435 000108 392803 976346 136206 688260 148583 756897 300756 388282 410671 356086 841176 455365 186315 930930 286312 444237 905775 398559 482969 309390 853059 818604 404285 302413 020836 967880 640560 808356 733003 021415 943448 761796 316310 549937 256469 110154 251194 746878 654630 302958 206630 248993 196473 362870 246956 863738 021348 642397 000552 979778 425985 299038 110710 393557 261388 655240 946381 502885 202225 285945 961416 916667 503721 969610 284060 377088 / 2945 > 1282966 [i]
- extracting embedded OOA [i] would yield OA(1282966, 2968, S128, 2944), but