Best Known (51, ∞, s)-Nets in Base 27
(51, ∞, 114)-Net over F27 — Constructive and digital
Digital (51, m, 114)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (51, 113)-sequence over F27, using
- t-expansion [i] based on digital (23, 113)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 23 and N(F) ≥ 114, using
- t-expansion [i] based on digital (23, 113)-sequence over F27, using
(51, ∞, 325)-Net over F27 — Digital
Digital (51, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (51, 324)-sequence over F27, using
- t-expansion [i] based on digital (48, 324)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 48 and N(F) ≥ 325, using
- t-expansion [i] based on digital (48, 324)-sequence over F27, using
(51, ∞, 1383)-Net in Base 27 — Upper bound on s
There is no (51, m, 1384)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (51, 2765, 1384)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(272765, 1384, S27, 2, 2714), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 088374 217075 230652 298492 467772 140351 575805 044327 475645 457180 004131 548347 404826 146973 908562 856704 984350 719549 573118 469293 924958 703016 725188 971097 095144 461964 695274 304372 722090 572594 030884 769783 285245 338194 368059 437811 994301 955508 966290 254581 859943 665864 064693 943095 442690 717687 047476 419174 718004 847544 795839 502535 423153 978930 410185 961812 450307 743951 149611 348828 490580 550544 896457 417876 920765 282291 980014 606509 258086 448649 138840 708085 551637 400314 442520 298675 458233 031649 911078 192871 762655 660269 640600 607529 896704 632577 510760 409560 048878 972922 635875 173180 250055 509809 601040 501317 008397 321620 027616 294396 293574 325343 610591 192191 926450 219538 232987 969464 673570 968794 583344 810054 448965 253468 160251 751356 188799 683667 727535 326715 042975 266268 634785 589797 128537 602903 855769 398908 898485 330560 760518 722150 496732 376698 318711 760537 793249 532824 253938 274524 702008 739042 900541 291426 556593 472181 937852 496371 744535 584198 070670 862426 006427 330725 769076 243413 841763 737872 449126 307733 029899 162227 823435 282854 508212 139416 022847 676140 253985 057036 366298 016066 573558 240776 195583 464667 076810 330142 399601 546978 418217 136484 938343 473826 277742 268996 348657 153568 024196 321851 189062 548836 660884 312220 332715 655571 104017 805420 774566 456468 707246 645648 845343 187647 632479 236509 080931 810828 957986 521323 382277 339860 152753 160014 819983 467195 349490 506123 661552 146078 848662 403131 271471 452929 781641 186706 242548 221965 256596 247447 423837 371756 506734 754357 943930 890949 050793 410248 498535 559249 816091 000572 742411 697773 859760 506094 120297 562500 222499 193966 558587 338309 846035 628979 528438 485396 737658 753690 750975 291057 314633 420310 388592 203549 403483 613386 148351 977934 351754 952105 327171 117813 995304 427323 307981 051521 666045 468109 779224 435467 766730 242431 742900 610944 350419 516159 311854 957758 756930 995457 264466 302522 514990 465190 216674 237062 570843 935956 536303 422947 813930 710922 672780 355422 096811 096499 450998 722135 459329 937019 988852 570248 129954 842876 102216 727942 329191 986976 293856 413092 609762 456206 428881 115085 061159 449862 350599 132611 138102 434161 181852 544102 483162 687947 313288 569458 849778 997793 763377 150225 275853 707337 016644 009656 668244 567205 716529 658943 726464 153682 137929 356688 677018 813307 158721 301988 336775 936679 333260 793135 588010 562159 140362 692151 740181 410215 361173 801225 325148 417332 613086 529247 570838 620802 264788 796502 331038 184296 937748 906993 712320 546908 513749 854771 548381 778295 348932 669000 471060 219609 721816 331448 547747 679669 323750 316662 256592 985704 147122 545710 460537 727717 059856 152472 637716 180975 364641 865710 106755 342253 333440 848610 757947 999618 895806 313626 917321 146945 012544 765477 605843 646229 078217 016253 225779 175341 958289 504052 032020 096728 317024 101183 618822 131521 983226 533548 894820 636578 274960 050815 711974 481867 500275 514598 482298 573222 898305 278196 902258 109150 274806 274498 256187 954818 225463 264289 294353 784595 567384 012931 462884 902208 881623 181664 867892 341744 039341 461660 173348 256862 189951 909377 984111 577962 234580 681602 149555 141691 512222 417571 058537 034924 225417 270044 314331 652605 094857 496858 928593 079228 416626 902082 047236 716013 802601 008785 714388 909097 038555 166356 807590 893858 078562 393312 602857 299788 204940 622072 985150 790312 530258 393002 869314 092171 921459 087647 940812 352310 742014 355438 485318 311930 278354 653614 609351 370695 326887 823255 984329 935847 259706 907884 277980 772798 214281 347802 656494 584146 091245 456121 972827 700692 307107 965638 118261 918507 510371 058283 867264 110844 430874 041434 319351 887987 340466 117801 664715 975806 631749 331307 061232 519364 958462 069547 696394 811352 785952 338407 681952 739955 758451 242650 029103 126686 082825 811785 653306 414788 073999 394795 685486 577013 611554 989149 484202 696201 903634 297340 554725 238446 109608 033230 089050 202688 746405 332889 737343 694750 669842 361313 055596 948232 776488 827531 123723 620233 943842 331119 877039 386350 180085 955372 749771 092955 774012 422672 141669 002041 289471 552564 355485 934477 577559 578490 089875 419203 346634 577234 453217 629424 825108 548125 902164 077596 548375 125219 076456 451950 252496 499796 398803 074219 849670 005360 098656 282530 054185 085151 383083 891371 345215 178566 694316 080391 441141 285637 703358 818577 638868 722149 / 181 > 272765 [i]
- extracting embedded OOA [i] would yield OOA(272765, 1384, S27, 2, 2714), but