Best Known (57, ∞, s)-Nets in Base 27
(57, ∞, 114)-Net over F27 — Constructive and digital
Digital (57, m, 114)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (57, 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
(57, ∞, 325)-Net over F27 — Digital
Digital (57, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (57, 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
(57, ∞, 1540)-Net in Base 27 — Upper bound on s
There is no (57, m, 1541)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (57, 3079, 1541)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(273079, 1541, S27, 2, 3022), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5 459013 607232 739630 925954 121795 339076 125231 218538 096746 020983 868212 981990 636774 983395 285979 719482 981122 836566 349498 479527 076275 248431 065980 263576 364035 488428 054320 253853 647073 176231 646648 291197 631797 037502 061390 400469 549862 578650 658137 713046 053999 334716 868069 242172 779389 760424 722805 617198 532721 027286 561241 868224 574503 588972 080011 862928 769926 040237 114573 605355 596343 352889 192274 839324 978505 576945 588224 347433 188613 184540 256045 807288 407559 349854 981091 593739 422191 559360 837789 427828 610672 979629 042322 419397 890745 327510 325681 559265 520885 405374 180118 115482 243681 778996 075522 157419 344395 749995 847089 870497 285377 521961 170443 299188 351336 423367 645929 905289 288571 316102 230377 467482 586410 219431 821712 678950 197661 312536 148947 503652 381430 893079 786726 958097 792255 417915 973305 200388 763857 757530 516901 275510 743130 266009 587178 696199 768537 677004 618847 033977 811579 490998 045320 319788 638728 636181 653140 810679 143824 511477 676283 932458 728746 579160 462542 943399 022123 987793 198401 521510 177398 763796 065251 966107 642514 954292 827166 080010 728364 925162 588501 615942 795828 002708 008110 649721 830022 190754 172082 955669 645256 878473 592869 077842 852908 631007 419164 247439 284143 712221 953789 248897 075850 911655 864366 586656 759737 749727 010825 344264 754340 605922 452765 952168 894559 253735 705615 088022 974095 524130 721624 701754 509748 136490 550889 725594 128941 319912 313263 140858 493501 639458 094085 110558 358314 156290 033326 093528 663362 156713 177040 343294 629769 607883 327619 240243 692616 663219 610333 949608 577020 292814 602512 550670 734285 150244 707699 850868 509571 485891 959053 889873 624843 050971 970367 046012 352710 227745 448625 383044 754221 499587 334127 639183 456300 505385 088449 271385 413247 735286 601318 353232 435122 035028 808400 231696 456285 023562 499236 502203 630443 631149 329579 303203 973802 312257 256016 194612 956268 288999 801775 735188 044796 168294 774327 425589 951972 302858 677575 682191 150964 829842 326250 279121 550448 467302 941296 434265 644537 862245 676747 014203 493834 172776 032545 820801 632448 611113 395709 195026 319491 247008 638191 996014 608864 260391 329823 396749 594728 597463 610291 107120 804370 113600 182267 057178 104508 906868 708071 433395 814461 420590 734618 014781 062161 226370 504825 373702 536847 761922 113751 884340 201380 226420 339938 483905 300554 026836 571124 924838 127568 021096 017113 111223 720944 498479 218388 854311 328306 922828 546839 502920 671891 561235 413237 171204 740308 538691 403489 454352 449506 879204 068739 415746 953636 411804 772558 807199 924257 829214 323122 568289 192086 631060 761029 174782 413566 963941 962203 958031 452443 367567 949750 055750 716849 667589 590146 548266 231164 049491 827059 799877 141657 913043 349593 758842 960334 847087 134159 223064 181672 272745 095827 511341 052968 054115 520668 997043 196728 040599 505803 300571 733830 924969 609100 095502 385698 783884 685640 675844 963867 112446 790387 069931 513321 988957 684734 323999 931851 906918 843833 875096 134605 598441 223863 518791 400268 540280 993769 132830 010885 607369 285418 365755 198741 936202 000070 121948 683254 711821 820464 011585 784765 722644 028935 156438 838794 960366 120234 007518 660730 365742 794844 826470 154040 271400 918367 358371 366140 836875 262231 370207 910784 060371 322069 374872 457467 816430 705010 963866 449703 421349 588604 218319 366704 163195 644222 995720 982224 579092 803038 875300 278224 434033 163912 346452 390659 930116 543588 244638 729749 584419 824618 740776 933431 471814 153352 590765 151365 459054 815650 758985 362835 576047 463430 819970 759037 502468 850653 428033 674971 303310 031515 043165 376865 050942 768201 769112 900736 711209 572251 805360 847860 996561 888813 294984 245177 949229 910767 558005 341188 986256 416483 196755 011577 135031 767833 701764 864374 636604 242364 647875 152209 676998 096143 082004 366005 281281 754843 588851 820515 008982 448605 240378 790546 493436 382400 062733 541376 292879 955111 290269 280034 786170 071610 391104 976982 852935 752118 635167 676059 080906 801139 041870 370326 883335 310519 797610 706116 870165 154712 670843 514475 050221 998391 464372 468110 032978 174355 392664 407437 847815 780278 510025 685558 875369 173322 571324 435022 718798 359604 685133 462041 852820 050941 555705 529217 986896 274726 396368 236896 271532 687717 715138 625276 900829 777698 079442 489641 104389 780212 591866 356090 757163 176642 561766 893527 129162 222810 947648 092089 259831 154452 551958 387057 614182 124617 414502 018294 515674 046008 905066 652815 468002 922026 300202 758784 646624 175755 492733 905240 638766 562077 031803 950002 601902 203805 941763 594488 722256 837824 026412 214580 590753 789878 446588 228340 164687 601453 680039 970403 716402 967390 845224 529062 335504 613392 035093 343644 547498 863876 881383 058674 103209 296404 302579 046982 362305 823348 903259 950601 366941 386310 406281 947803 879914 767491 558881 592882 990738 916566 028818 983767 810788 933737 / 3023 > 273079 [i]
- extracting embedded OOA [i] would yield OOA(273079, 1541, S27, 2, 3022), but