Best Known (141, 141+∞, s)-Nets in Base 8
(141, 141+∞, 194)-Net over F8 — Constructive and digital
Digital (141, m, 194)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (141, 193)-sequence over F8, using
- t-expansion [i] based on digital (85, 193)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 85 and N(F) ≥ 194, using
- t-expansion [i] based on digital (85, 193)-sequence over F8, using
(141, 141+∞, 259)-Net over F8 — Digital
Digital (141, m, 259)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (141, 258)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 141 and N(F) ≥ 259, using
(141, 141+∞, 1014)-Net in Base 8 — Upper bound on s
There is no (141, m, 1015)-net in base 8 for arbitrarily large m, because
- m-reduction [i] would yield (141, 3041, 1015)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(83041, 1015, S8, 3, 2900), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 58 130825 961357 915599 480430 654966 392204 562339 543217 415275 567316 320933 890561 526611 421596 506507 298306 331198 052766 676418 811054 633729 381446 783773 183422 479791 132345 415066 282327 963922 928863 489146 148117 663473 988568 822853 616530 571109 620448 584688 836843 967698 839316 299455 981096 595748 712171 933905 029336 346130 560650 209665 284267 962451 395310 565530 497107 214268 480597 344433 332691 544005 228950 079553 118191 082383 713479 732806 434089 678022 869921 344436 221885 836239 581711 043889 619718 215013 249843 322004 785195 608517 352152 840886 852855 174842 865265 090160 333917 255336 240200 723160 758323 185998 147392 553505 006907 942184 294738 339854 946799 300049 480478 874841 291746 751890 119552 304385 205307 874296 008673 189090 210082 557110 007797 316186 761570 416375 124402 532970 257973 655017 018395 222487 050783 846276 768052 073281 881274 320983 926981 514576 307214 800224 471640 184873 950703 155274 718184 870898 515347 698787 072813 598833 154917 706609 092127 141723 928313 436144 773753 988805 972417 320384 111804 051241 371097 805485 792544 811306 287741 934317 054719 516718 490593 557468 272345 379069 340192 823841 558332 113591 440298 355904 212086 418374 624271 555251 636864 472118 811156 493433 899433 007202 623461 628620 123689 575994 610087 970277 712332 119250 424829 011166 260217 538749 662850 625208 311142 695993 238714 801858 262475 314406 584099 123647 667424 645811 326635 577522 553163 559742 803360 059789 784086 691615 922775 897991 525671 981437 854949 840168 505118 655627 835237 908290 356572 963208 822500 184570 302073 710315 252269 428424 347179 553828 312607 303073 776750 521941 826363 305802 702390 179203 126033 173319 334664 194981 033761 167966 390353 973335 949516 939382 125930 808969 323927 129010 951527 019074 257934 138328 687801 140716 969085 455041 559840 670548 705522 758474 997479 652455 462038 666725 056472 454514 481216 068114 154037 181204 402107 810038 533462 516688 695688 337486 604346 118868 328392 239234 181491 244052 184440 481399 462616 422247 222060 231402 003259 834207 731543 483955 870926 448204 183837 755484 566247 411465 349262 112931 058532 629028 915600 017895 647906 232362 392806 364912 364789 131538 618099 269281 089748 161447 729666 987930 539840 183191 486547 047929 175405 241929 147633 896294 126596 609640 301206 351390 372158 908424 757245 037791 247945 249322 624611 408479 484520 973752 001558 863248 903369 339027 197331 255037 781714 166278 536264 559225 206268 794596 295972 251989 323079 402964 189457 289105 070316 783941 857337 019378 162310 600529 621772 823240 135195 040096 269464 694411 578698 382600 863411 391008 518252 448681 623492 138697 699233 859788 990870 640953 079735 092523 839785 512805 774803 564865 013124 632650 395922 491151 390471 663195 338068 889265 608645 772887 670738 515842 175321 506509 152457 530354 185386 870946 364304 048788 082688 390018 878371 141975 581231 881321 615809 401509 969831 814379 781265 163993 921968 077010 303279 006337 184505 080768 199449 975476 301361 562238 997103 577199 716807 341190 497637 512704 500828 303819 193978 228330 096308 303287 370356 288914 630177 828476 436257 311245 461675 511893 721088 / 2901 > 83041 [i]
- extracting embedded OOA [i] would yield OOA(83041, 1015, S8, 3, 2900), but