Best Known (17, ∞, s)-Nets in Base 128
(17, ∞, 288)-Net over F128 — Constructive and digital
Digital (17, m, 288)-net over F128 for arbitrarily large m, using
- net from sequence [i] based on digital (17, 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
(17, ∞, 386)-Net over F128 — Digital
Digital (17, m, 386)-net over F128 for arbitrarily large m, using
- net from sequence [i] based on digital (17, 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
(17, ∞, 2322)-Net in Base 128 — Upper bound on s
There is no (17, m, 2323)-net in base 128 for arbitrarily large m, because
- m-reduction [i] would yield (17, 2321, 2323)-net in base 128, but
- extracting embedded OOA [i] would yield OA(1282321, 2323, S128, 2304), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 16607 456489 979869 900870 640127 589423 048325 181996 131979 195174 094004 527244 985004 285533 642453 808876 090719 423739 888709 881055 960001 531859 109334 480734 628842 102572 724244 340094 090600 000779 491991 102434 050313 681079 994849 588946 060267 900275 674946 346845 632042 565725 196039 563566 133293 794006 505600 004653 399385 327788 480576 261614 256904 999979 770330 583162 179610 982439 398406 466980 076995 594251 958237 688475 175129 873597 314498 181948 944459 932953 274578 941584 333854 563353 151174 943556 584329 960790 413276 074843 928801 697323 649575 472501 590001 332390 552991 230378 861636 074093 992447 734762 672647 252758 318404 432120 424658 134736 630918 998345 168688 200141 683952 679033 983679 665303 953050 774354 227437 941111 609995 747933 272031 280276 354072 037096 578070 322931 751160 366717 761742 876304 952037 317558 824774 572299 649117 183114 707686 766713 808871 246504 951715 382510 556350 526675 973839 606823 119880 285253 207182 171844 782910 472682 636186 414780 790946 172070 387021 958814 982349 391635 976108 501014 230192 470855 237517 674942 941160 858971 705434 668393 303607 097827 235863 422536 901525 470039 388973 993242 441935 894971 632153 883841 888263 221599 778962 149201 440103 552949 336219 995174 204854 720959 019776 332704 894269 669962 485234 655800 527383 050971 806058 305187 177969 564792 252112 772633 515335 883239 150225 274789 774467 575493 101758 287805 235670 691860 995466 807548 183646 831312 244946 023273 053272 358476 402276 354156 803243 432153 679624 403120 525653 056153 337239 062328 199628 017272 726264 800099 991611 101181 970757 982077 106078 101565 394144 567848 434067 257611 664941 837435 914235 140478 853522 789053 972011 667765 312213 402183 967883 845688 981674 940276 057769 063072 324094 651590 495241 456858 872191 918854 372795 500251 997419 416251 817640 561442 804216 678534 791021 707987 791863 764306 438252 310840 436120 945946 489628 737249 023228 503774 209449 382279 449448 797476 295610 783583 629562 826912 528975 206116 138140 986230 650958 787371 513066 912888 041404 980934 600549 787815 976647 068239 371841 976830 068675 376520 717428 566778 990153 665786 639296 656987 431703 169658 573752 130330 134425 321811 753011 724464 055328 071707 134050 255191 345652 811298 600297 952369 737374 645817 133680 837287 820707 570991 325323 186276 267810 734378 264429 085025 697030 820745 952149 745052 782794 035768 116487 762438 922670 986746 234595 603384 733554 548685 770880 229020 939016 002650 167961 732396 299288 496576 705782 205190 483770 713782 753996 364231 576768 979372 243426 180964 773959 394688 609623 422979 246557 737773 744111 083666 921331 936288 274264 555445 336785 046716 904287 392470 167381 853271 611734 328309 441668 781754 182869 469321 748313 662755 851966 421746 604116 834418 760923 109785 251057 676186 896091 693543 206351 705563 113792 706483 273795 350840 450243 571280 169819 738972 088823 038105 642764 856907 620847 847650 734157 613166 271920 506540 444725 931177 722527 787504 625326 319606 350811 067579 649749 587523 673919 555758 126535 833971 867837 689465 092889 740453 192721 481058 785242 343134 846173 111234 835201 742435 033762 045201 018737 015883 946094 266411 865661 361369 697071 189299 272476 949831 474437 952847 647135 580990 187991 954376 514671 204706 647292 129373 319000 405930 710322 296145 355429 316074 058827 432891 866780 997913 691180 613217 571411 414166 370692 218763 835330 989153 897627 086606 596336 939017 330875 468176 380810 152114 341951 785712 021628 382971 750139 134353 419271 984360 138508 629826 128183 479174 568022 422408 702874 671518 758539 060892 075036 445976 317850 367544 235101 778429 507905 077177 103062 970577 074013 838273 081502 705356 478450 865894 024961 528167 801987 065966 221434 659401 921018 480407 636095 239792 897260 229855 831505 423732 530030 662411 292858 590826 660557 743673 148935 154142 095306 973158 250290 259529 385053 899498 565322 076873 062803 548272 978814 914916 687299 083073 311019 273991 779037 113602 529272 459152 732902 267185 723926 360060 369356 350551 855007 346314 850356 743198 282764 011062 936035 557392 907602 267791 473646 590737 045083 742948 089548 211659 874260 636860 101052 431644 512915 616941 504811 699574 071735 605878 399968 081943 645172 810396 937825 663867 698432 954267 135341 044092 218448 380282 771505 700777 619697 071951 300778 454632 855049 863585 670819 589045 045382 312278 379877 096959 490223 313601 359398 425937 850753 011939 401574 954102 623557 691296 491837 507903 926687 237885 620337 492138 765431 338026 376273 402817 858960 294923 012305 597335 521162 221947 574594 279813 853035 251262 493377 372763 181495 887281 924971 438813 371508 729774 716927 661073 686772 380962 787296 350690 536306 088304 597547 360601 983659 562719 135096 264224 923361 607489 412629 834381 082223 967496 067276 425030 437649 252118 014569 700996 350200 787775 629742 548871 830432 009852 479842 698973 669141 202997 148510 698672 046673 640241 133580 865433 545673 811118 004459 966325 398327 336716 919779 371708 249961 888276 586392 957211 588528 749034 662470 908142 185400 355620 125238 497732 647971 429518 146054 942200 928237 532336 125703 385527 052360 393649 544916 374068 982170 253271 767500 097920 396408 595306 742234 687561 851412 512351 862646 506971 402286 422364 638945 215190 461027 848379 699912 073133 146170 591472 394176 559636 544681 158928 572622 623894 155412 736241 981124 052759 678705 839506 035214 394208 390797 609035 603356 288820 317244 091444 862416 845180 319221 505544 172860 671548 817879 160697 638783 253514 535406 323698 921726 704593 897774 234864 888261 855853 647778 508001 822198 318620 796776 349696 / 2305 > 1282321 [i]
- extracting embedded OOA [i] would yield OA(1282321, 2323, S128, 2304), but