Best Known (144, ∞, s)-Nets in Base 8
(144, ∞, 194)-Net over F8 — Constructive and digital
Digital (144, m, 194)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (144, 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
(144, ∞, 259)-Net over F8 — Digital
Digital (144, m, 259)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (144, 258)-sequence over F8, using
- t-expansion [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
- t-expansion [i] based on digital (141, 258)-sequence over F8, using
(144, ∞, 1036)-Net in Base 8 — Upper bound on s
There is no (144, m, 1037)-net in base 8 for arbitrarily large m, because
- m-reduction [i] would yield (144, 3107, 1037)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(83107, 1037, S8, 3, 2963), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 365887 367672 785630 712343 718505 788594 512627 539252 304516 040581 367828 757826 557005 812544 089030 132714 019059 020780 481341 799491 861043 110859 274098 268219 091283 213708 224047 927070 426517 896661 697554 267307 081475 058468 911901 423445 573166 347948 607549 579235 518367 408727 295191 633669 135172 437415 091195 971946 745299 723777 004663 684315 854461 596204 895270 577412 637705 891693 609381 701472 451729 161816 010182 878996 100099 472288 281185 890410 183567 410340 593059 610826 550467 275174 566472 910437 951753 322530 198807 081075 620158 964101 062940 983403 823469 858458 063877 804025 812376 500637 432091 393853 461819 159136 022975 238679 227264 088123 588420 640392 448935 335758 123753 771659 885029 407879 084467 013907 448652 187589 172628 287416 979563 742005 169365 684399 905008 420404 721242 280109 716002 858070 783955 872794 101854 785164 639585 448958 489277 317369 160020 246936 937332 752483 944450 750877 549608 867109 158486 079554 057298 738307 869674 626918 585574 045569 829150 904063 708460 905396 083618 675384 056890 210625 403090 288380 987581 908214 383167 680496 844540 138177 638277 162724 602715 177472 747296 221119 557759 129804 038236 792183 747459 713655 537275 378612 879608 377171 634439 495021 607396 469164 774643 675725 190723 330494 161625 932146 837171 154141 987205 994349 453861 034807 728623 504795 433387 436355 431407 215773 545710 031965 659131 253006 794621 527268 467500 470625 856812 077574 683322 476952 697376 419624 121865 517723 572649 482810 605630 985629 544590 082939 495834 891130 576867 070133 873011 349937 234446 203024 070436 642702 494226 719466 367099 456804 590897 946753 442379 193948 629210 870859 246045 984026 343380 866814 603398 343701 602005 820787 857348 283458 786359 958643 087145 323933 545583 264150 526465 028633 198630 686531 841868 727273 545012 431677 268231 353790 765216 398453 264478 460580 107224 165070 288486 405643 302639 348338 000116 528919 968968 771532 075340 450274 606335 571801 272057 004518 435173 795788 765309 326884 905094 242152 109438 247019 661809 635374 547556 389939 464654 159985 411460 559396 101008 827968 426827 551816 263724 914818 605547 562703 759822 891559 184113 984863 266584 127291 426646 285875 652651 748685 316898 011082 743868 899140 286337 685220 932413 832150 859080 001576 843002 646340 609609 300790 122030 539975 277672 794475 461893 231873 392730 086468 680232 695221 582073 993673 728062 545715 582781 105317 546195 345458 093740 886327 335504 523295 598685 915366 537595 231620 663079 030972 573536 157813 069146 838222 443625 195016 867491 165479 867069 121978 360548 640254 692247 319261 493158 833434 399408 437974 249304 973576 224051 742145 524717 611376 742490 525801 604022 508783 489290 561530 204475 195988 109243 087200 648788 098789 098859 896824 229040 453149 938101 336356 127543 467327 509075 479608 651630 559449 675716 837903 352071 979997 872601 833092 065150 805493 443900 267163 424081 147441 648149 137047 052578 673362 134709 547987 593752 919349 270118 356323 760449 978044 484307 713629 719330 072961 977657 872113 165341 864764 009343 792151 348243 500015 778202 280279 989216 650170 930096 051480 804648 951110 123469 894006 705323 613890 986651 047827 293804 915697 532170 306267 317369 044992 / 39 > 83107 [i]
- extracting embedded OOA [i] would yield OOA(83107, 1037, S8, 3, 2963), but