Best Known (18, 18+∞, s)-Nets in Base 128
(18, 18+∞, 288)-Net over F128 — Constructive and digital
Digital (18, m, 288)-net over F128 for arbitrarily large m, using
- net from sequence [i] based on digital (18, 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
(18, 18+∞, 386)-Net over F128 — Digital
Digital (18, m, 386)-net over F128 for arbitrarily large m, using
- net from sequence [i] based on digital (18, 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
(18, 18+∞, 2451)-Net in Base 128 — Upper bound on s
There is no (18, m, 2452)-net in base 128 for arbitrarily large m, because
- m-reduction [i] would yield (18, 2450, 2452)-net in base 128, but
- extracting embedded OOA [i] would yield OA(1282450, 2452, S128, 2432), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 182130 989774 130694 025479 349990 960587 087367 186787 258833 895750 316645 831041 343947 053358 768140 974839 185158 720307 487160 450178 668975 273661 127663 558682 055727 916641 494000 127805 975767 528372 661156 646186 759539 810595 336426 276009 909747 938966 688297 083933 013076 559388 672471 875403 302956 193316 434774 101466 914402 814257 189746 657017 290029 769758 553680 606139 964265 506546 134097 510041 560686 615517 509764 406656 911277 211578 824442 849106 645068 883885 803188 212044 084713 767854 201144 603467 139263 179568 388152 226902 395295 039936 692784 299638 075891 727209 415851 178558 318052 803521 172026 636538 641114 910606 019220 470947 804130 253245 391607 563710 563624 014876 118637 769876 947119 653787 919095 325520 944128 100883 212066 053888 746115 169394 247107 195569 561391 386616 047916 908171 933903 045745 377872 707870 133792 779758 191126 646298 804200 566577 282639 955042 693283 939050 509794 242387 072979 744507 415933 984282 759420 290872 895411 711302 403045 909116 330472 453988 944873 460079 387119 935976 484237 609211 266166 826864 557604 316815 144075 578067 702371 693840 322052 928077 930689 208246 204965 699921 006907 296703 372195 005684 234672 275834 362166 990516 259919 002893 187360 210622 884263 658903 783509 691204 265171 993366 732137 207087 344277 759374 928288 917290 357660 450123 478601 224143 580675 888271 793137 615759 128803 656586 537245 926278 127955 401846 358560 144684 221664 058199 768876 300821 994998 375755 299934 498775 088445 293246 349993 070304 605145 776433 948691 435677 227783 338735 331674 068490 731464 932500 299728 029686 037456 418369 503585 062389 526812 267149 368585 269190 384980 027430 764390 886286 916317 542263 253437 855800 273906 560963 279931 359068 407195 617499 604610 712622 301431 354640 801413 954379 647460 472650 603335 917568 748668 978028 901975 376103 963298 792299 770001 792741 827392 173207 754045 583543 096464 299189 897582 299054 034920 079786 916677 760116 113749 077519 059903 335618 179238 920342 893457 832320 093899 180510 229615 917672 618800 615459 960835 003834 258530 082829 330896 109703 274411 004895 008104 880592 516214 113543 259147 727035 375209 824019 263520 088562 083437 715688 294985 606953 209441 538477 999800 176799 365309 017923 023677 528463 945355 747805 728516 478723 961188 033057 229995 994762 148155 994718 139096 386837 510468 769507 105705 348711 022977 511657 117306 806237 642120 904060 807034 436059 816390 155088 305776 472573 556832 595116 247655 890291 147345 936842 505112 218438 460566 114729 530070 820018 532417 110584 810018 221119 208909 646311 146937 136953 653200 963571 023252 626499 589032 254681 344943 270111 692643 705039 068670 920111 936291 347743 466682 305077 700029 554218 492949 470991 499177 023111 005621 927153 373922 347868 106712 018473 298408 260437 212997 362247 284912 805321 919643 319955 387487 056438 878151 685860 325866 292714 671588 551487 470854 408224 912171 510075 514886 034864 696991 028327 741777 961430 972816 661481 780578 324740 058543 867868 538482 754282 630340 870369 342972 728084 971238 345980 097394 415034 310340 458380 549259 074837 152285 955979 447202 902462 325406 477836 450637 909448 543502 568485 290866 787130 534985 029602 054440 612314 266410 059279 197136 250177 141809 153822 818666 442413 067059 086129 438445 647117 630389 397367 542326 203161 456199 246224 373008 948491 378359 979926 013921 697042 796136 859160 001855 271042 716504 473438 487120 393753 249316 759413 172364 339967 743833 811747 999971 287760 769104 943919 487510 213855 770944 700937 435383 507752 877400 444424 022078 410634 739935 762631 444287 946310 262759 775022 690186 461163 083648 211807 096131 958894 635470 130387 471737 373708 623212 597133 709000 839204 511670 827307 131004 819701 184555 853445 384577 097303 203801 911953 518243 109625 637630 765040 164475 392209 450986 681392 177688 633039 149035 005087 583938 865023 898488 487918 707034 530311 962913 934561 412889 362790 263789 135277 682379 034289 671941 652977 062378 988345 009145 651892 889835 161364 432825 878684 442306 504767 920890 636550 087655 562097 083358 566191 470506 041532 678872 998558 730745 263196 392290 621697 059949 424405 728979 176204 305294 805317 187471 180193 621480 907164 414484 677826 111805 640485 139013 671839 201749 763926 739985 542845 352110 906304 829780 318097 955040 051226 991916 441566 273679 946548 332803 420085 452517 789772 425806 527072 221005 068357 366926 478692 854160 577329 227264 656467 469928 898550 904386 110762 506582 580095 612920 067688 221296 502124 611472 285079 946194 289138 676418 942085 695390 757371 818689 783676 817261 644925 065170 232360 041147 139473 974491 544341 685265 084483 553553 922660 289916 057141 658995 501426 770937 246584 251356 503067 569152 820632 483567 987916 140187 461431 136484 809185 726625 888581 924583 245851 287086 733098 866173 223530 601433 680063 632806 971679 016347 124524 052130 391924 885233 408433 064560 890619 807798 860917 423372 209593 466618 549772 189779 778778 940410 520394 869334 818797 880899 521404 503919 091025 148832 427931 094845 466519 979897 257283 224335 489019 949240 549420 799640 912225 447554 215722 211342 173300 335447 964037 830215 229224 255914 142689 893302 698584 915121 409008 820335 816830 313386 472428 473357 564244 549157 824231 945305 012701 054021 383386 833488 770462 897965 108929 045802 036497 888006 490340 817734 267434 315690 858794 683396 157055 739925 417717 319292 349518 082520 404668 546113 515331 050612 139873 503595 007291 496144 192696 549915 378649 042779 875950 187732 021891 857262 176611 339378 713095 969975 524757 788136 009869 362132 461941 839027 644716 460792 546240 124969 765488 076227 089410 645746 330118 355801 613233 421868 337753 228295 601528 629478 097073 937848 867064 828883 223723 404410 457490 315382 664072 314038 876180 217986 745115 101150 945773 763729 123170 963946 237499 943035 660472 665747 615598 089588 169692 090784 343790 774339 216267 453165 489514 886406 979652 157440 / 2433 > 1282450 [i]
- extracting embedded OOA [i] would yield OA(1282450, 2452, S128, 2432), but