Best Known (147, 147+∞, s)-Nets in Base 8
(147, 147+∞, 194)-Net over F8 — Constructive and digital
Digital (147, m, 194)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (147, 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
(147, 147+∞, 259)-Net over F8 — Digital
Digital (147, m, 259)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (147, 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
(147, 147+∞, 1057)-Net in Base 8 — Upper bound on s
There is no (147, m, 1058)-net in base 8 for arbitrarily large m, because
- m-reduction [i] would yield (147, 3170, 1058)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(83170, 1058, S8, 3, 3023), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 193 473041 162560 117529 212322 217365 414336 320181 442968 712432 747907 628982 026284 759324 310476 974347 953684 762396 805193 589944 856263 127068 241989 054839 087408 119348 114681 703404 433768 368220 338639 848629 158270 551320 967975 526566 655388 783692 128152 863176 368367 855496 555539 767510 385665 437618 780326 616413 551814 709136 773157 931165 158664 307452 931125 293436 897201 194743 825251 322068 081584 963603 962183 644593 392918 613820 056484 746990 363195 052635 356174 886932 667797 855817 698454 916896 299470 466241 297149 884997 343768 293933 498042 835758 841458 791495 185156 896358 138464 255715 855956 356369 191139 318892 973394 070227 658901 700470 770077 522317 594499 732263 022461 416171 981311 306305 515864 182684 200967 781623 459029 884949 628816 621581 993476 182342 187795 295641 506551 496086 164991 819119 005478 518460 095303 139642 640169 335636 843751 102610 434008 308544 753758 712568 611249 653391 553354 631025 277331 124595 388611 796148 927216 571158 979010 649244 613010 024974 613906 584664 767807 555740 658685 539461 388407 944767 967894 046326 380546 870805 473530 114462 888916 006935 708200 596111 437256 986445 240885 413306 964633 639260 737566 225207 817577 436784 358012 597026 573850 049946 202578 325480 695182 038360 022789 629462 980919 770808 364231 741585 579211 604522 598908 086255 429990 073648 516977 165717 608290 653535 024643 567401 941581 736290 002688 403872 988913 576651 317185 430384 597145 042244 462991 275954 235407 687533 855991 813450 620274 017867 810851 797212 418811 800217 968955 631514 898977 803104 959789 386293 955374 334505 769203 879938 490506 670934 998544 330525 474323 930234 997773 826053 804051 653674 715979 560151 266775 241738 490647 147421 430930 416042 310004 250645 258626 753381 917637 854507 183583 345308 383133 870398 201704 186611 929166 564083 994746 389682 098384 939506 015053 082273 970721 461351 411725 566283 846164 065604 382629 021733 629100 460778 499872 112059 989943 879782 198198 931981 285697 330942 100366 444202 960463 498443 211096 063881 243159 430832 308685 361338 624591 215346 386835 773114 469381 811372 851248 351988 772518 674512 438187 811190 584762 468004 648350 988523 428517 445883 612960 854239 724470 525761 874877 193285 214625 687169 604694 227581 118144 760638 141063 885930 370495 780630 819439 907494 718262 951722 817803 262959 031527 478302 696623 403809 825490 879227 461242 207394 564986 789473 086360 791754 809332 525114 185194 029246 982957 529295 861022 198430 564712 553842 089531 042125 205219 350638 149604 701210 660092 309772 371936 393624 907523 818910 398011 143083 302751 702908 475754 300658 634621 556779 452652 778351 727418 185429 680699 942098 130929 889402 789425 655511 806573 753839 082033 004520 684731 387938 803796 173029 110980 393451 628268 418694 534999 433530 384921 799511 583433 751357 593396 138723 620315 461198 471340 531924 564699 092720 011927 801429 740484 970268 893693 689484 946239 718019 769665 732232 425706 051983 814918 405506 351782 245163 733247 864405 293443 283872 378909 152347 971684 537592 525772 664461 084374 997802 712340 685742 220641 094068 975440 062827 542375 656178 542601 912386 332544 275577 180927 626052 970911 618938 981054 488142 362808 817494 035285 479013 018883 486099 739015 926431 291904 768540 989855 072886 725745 311744 / 27 > 83170 [i]
- extracting embedded OOA [i] would yield OOA(83170, 1058, S8, 3, 3023), but