Best Known (50, 50+∞, s)-Nets in Base 27
(50, 50+∞, 114)-Net over F27 — Constructive and digital
Digital (50, m, 114)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (50, 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
(50, 50+∞, 325)-Net over F27 — Digital
Digital (50, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (50, 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
(50, 50+∞, 1357)-Net in Base 27 — Upper bound on s
There is no (50, m, 1358)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (50, 2713, 1358)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(272713, 1358, S27, 2, 2663), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1695 943641 435463 689820 230647 422201 270445 563658 302827 331621 159281 106965 095228 818089 400710 467028 178792 621830 352063 898778 937122 925583 344888 250161 630866 960840 088886 694213 031130 214558 930512 168297 277047 613965 991737 995719 047299 788003 343619 528987 790538 208130 951167 955092 912889 897670 880333 620129 521909 016101 271523 430668 381967 896776 009551 600177 131044 438908 233053 847566 521455 458481 053271 458777 961244 598279 792833 713641 716337 937351 382290 192578 812052 970656 024704 551064 425373 888705 268677 156732 702992 127146 843878 565229 599015 781566 593604 745640 553861 098347 396275 279611 417568 501701 638397 283729 673881 639792 237116 378891 208124 061892 065676 148075 686193 084050 398576 097295 792121 783063 346629 979473 920282 550853 732080 766705 942448 490749 441277 327878 555543 672481 825827 351445 096226 841669 696031 481503 720491 535400 735318 237346 551898 986537 708831 780341 319388 233077 903156 759921 709661 242754 815342 955645 654248 199008 258278 510254 262702 956689 811079 168141 931303 960996 489493 753916 993429 556295 857858 031108 386756 651224 893510 485563 603271 062008 953849 551301 985476 833762 943591 218722 707659 401044 644310 201884 351974 891596 785601 849629 947586 192523 869203 849822 902453 773762 075260 957655 395118 948398 776915 881322 949926 454378 040944 608942 361055 110378 921407 764579 335818 115141 816634 056381 589924 802164 825039 077296 457440 198771 368834 689109 678243 162415 151002 879246 323996 588260 122626 968287 971891 433678 239188 028552 807577 605137 978142 208321 159069 470897 033409 032832 685248 474446 844019 662605 536280 835145 129639 393348 990269 745102 061134 024050 663318 854947 895003 121608 348494 168173 460004 714615 469288 625036 538037 763291 644153 305806 472338 351382 832902 720164 785691 618444 906836 927288 770902 363076 541127 185561 700039 946931 553914 207907 944684 759957 841575 383526 244505 369133 672995 323201 454664 795797 193695 195068 385631 413599 087830 864391 039277 124404 106885 527304 859955 777421 978084 033088 691252 431698 591980 126014 282375 431053 133313 525213 371136 680356 293100 489679 594527 552228 847071 942071 219651 067361 157550 407047 717590 129599 972050 156238 139213 234968 438113 722192 852286 205052 413203 544468 100603 562238 564057 102386 240088 752616 632516 445851 823339 024353 838060 545114 724431 555383 365072 144947 474842 783197 490192 576939 338542 315294 394099 153367 814712 801705 944612 822294 622670 972729 188551 308259 527936 815642 693065 239822 683157 245694 213179 352206 495543 133246 571938 418709 522565 941110 799679 823713 839167 144861 247689 308480 496238 058405 791320 495011 009151 679709 452366 457691 917721 257537 793212 645966 764619 106749 674916 339409 905129 718195 443840 456026 428305 535586 014836 884243 602942 698187 852316 033272 825501 666243 914298 951770 621995 377464 628396 252439 168387 017889 382599 069773 457846 245141 821374 256684 975024 101207 500347 306017 128594 412168 935167 045630 420682 470845 542850 078667 387571 954043 941294 374257 636680 174514 124528 696277 457671 908386 812483 910517 093841 115317 895478 453475 177953 787796 902469 209901 789900 653758 196587 758296 469957 820918 153005 588934 572248 494377 610989 108504 064276 981722 111694 544158 166610 179980 034886 777074 651381 146994 179596 915289 598847 762453 649331 401922 936194 376343 179661 601549 210678 922087 597405 851495 715059 109838 630721 018333 256303 467512 427974 415129 909097 421767 956988 054004 520518 554071 826444 105497 878417 697335 160711 120443 250371 279566 297858 637167 676469 631538 570722 071344 770423 815813 373083 160549 106148 548770 836800 231804 621548 546225 981966 601622 309981 023337 288392 043281 744679 310175 985807 088534 635769 773581 632591 759812 375886 932720 510693 640489 859529 711975 654996 047899 585376 830659 582861 220947 021085 518063 456157 304183 027449 683940 017579 513895 515821 635119 775237 586971 853388 961283 753308 784519 168386 805494 262666 340683 962295 866637 312937 419436 163980 529660 684933 034379 815077 731040 530861 009538 245228 510490 376014 914827 012454 593722 308816 700829 995546 732585 656607 604681 074141 629211 269556 968763 205993 424895 667821 163056 331838 543069 981675 569579 811060 820825 516092 229768 032456 773776 622142 532006 932088 932462 307495 942431 641813 636393 659311 276212 311900 156144 329190 472665 205787 596851 921314 828523 281407 960372 083107 431351 749522 470465 847943 066735 132386 513229 / 74 > 272713 [i]
- extracting embedded OOA [i] would yield OOA(272713, 1358, S27, 2, 2663), but