Best Known (40, ∞, s)-Nets in Base 27
(40, ∞, 114)-Net over F27 — Constructive and digital
Digital (40, m, 114)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (40, 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
(40, ∞, 273)-Net over F27 — Digital
Digital (40, m, 273)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (40, 272)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 40 and N(F) ≥ 273, using
(40, ∞, 1096)-Net in Base 27 — Upper bound on s
There is no (40, m, 1097)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (40, 2191, 1097)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(272191, 1097, S27, 2, 2151), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 17 360695 369636 046747 552938 124509 019173 826183 357472 211495 434744 510137 604230 232720 508121 443099 197890 781129 964590 655392 443377 258580 745554 039625 010953 327006 682155 786681 156024 392163 562768 562838 835519 692847 026597 211765 333109 933740 034963 989805 304365 836372 846366 707533 676790 563751 796418 840154 608670 543312 364751 364981 671000 030362 905812 858941 516405 250020 311515 225207 313630 192599 160261 445942 351407 389373 903027 643894 916119 582544 249945 778263 928103 195095 540573 346991 036257 162672 121458 059164 775352 139374 770913 257617 228584 644088 782031 505177 452352 884012 877420 904261 124516 563392 960379 225322 037554 592907 871598 595212 170264 178566 562815 741392 211385 981021 690670 214269 178515 185950 214295 906549 340760 722991 256153 135627 524818 110466 819004 953797 396017 985882 006215 028899 429919 919946 681129 567064 373447 460588 290481 451100 430462 757779 914973 740199 109081 817058 969723 225703 599193 979819 475474 804951 497783 654260 504460 946343 919185 293202 179387 763046 065673 532545 472356 950810 442439 470797 797681 187477 339523 645039 337293 440107 713185 872532 606372 439619 813907 189620 984621 717484 952978 117468 923262 253957 882535 637420 501315 437194 338666 370122 389008 637074 545606 039338 401542 659018 971834 459249 033448 312890 658540 407316 176778 118658 649406 340196 926233 211645 722379 783915 156082 516867 910916 671785 776152 943897 545408 920124 079221 872012 034589 733446 192035 092751 073484 277345 277045 482128 832018 601601 652042 439341 107521 429179 547150 512132 038624 981923 904096 691281 693280 615635 771471 595913 030454 916319 744032 143804 726343 769627 633336 163795 276683 492329 046306 736297 839822 758492 408999 805312 799339 686867 853068 950404 653446 018853 620251 355334 772222 250863 844720 551627 646335 261785 026998 739400 357171 933230 042511 473092 879729 094596 643766 304054 719748 237283 107417 411703 855889 901510 934193 831913 862852 087103 706789 680584 587238 918978 562911 837487 778933 577753 764525 707766 243523 822560 830325 251203 729163 022242 068217 601774 599497 980776 312769 061872 417461 054827 052253 492242 927872 440306 164156 857604 221853 217722 227891 935211 675139 717216 316991 895854 244459 287680 837637 763825 661714 508044 687538 641440 000126 103052 025754 940535 504152 859646 943402 113264 862425 964145 689451 556341 888198 361632 994252 758335 672461 725026 664617 578118 639973 065279 756069 075463 968465 026937 820584 313350 551704 095958 979603 012038 915217 847023 342962 377051 156473 763347 440859 016814 619987 954298 213258 491113 468638 308659 870661 984433 961329 010255 306865 136315 437185 910427 126076 571934 151938 184827 913744 105084 476043 423500 331810 441465 610489 318908 262239 750437 988865 946207 840777 712601 546203 838835 606506 071698 603591 021196 230029 060292 041725 451039 924333 956250 561330 000278 594277 051417 506716 639463 727028 739789 336983 594320 225302 625189 472765 428594 523134 046960 430533 706573 255938 537260 392394 336714 542737 155012 695867 715273 478029 911915 549713 161411 049058 336192 336279 644087 571977 021559 125399 210052 849617 079519 566050 597475 154285 292527 605443 011125 678197 539269 506502 421489 837243 275767 315957 821325 645705 530676 349648 580205 449889 084781 688751 388084 996749 288085 150947 686893 778272 448087 977218 651892 591350 874850 604075 462509 655321 667099 413756 674263 487758 219313 387173 097544 502622 264053 084859 395289 714711 718657 980512 044239 425029 808640 173632 802500 455994 550255 498555 687436 573230 305526 905507 680452 538798 427725 885999 745385 938584 582129 / 1076 > 272191 [i]
- extracting embedded OOA [i] would yield OOA(272191, 1097, S27, 2, 2151), but