Best Known (39, ∞, s)-Nets in Base 27
(39, ∞, 114)-Net over F27 — Constructive and digital
Digital (39, m, 114)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (39, 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
(39, ∞, 271)-Net over F27 — Digital
Digital (39, m, 271)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (39, 270)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 39 and N(F) ≥ 271, using
(39, ∞, 1070)-Net in Base 27 — Upper bound on s
There is no (39, m, 1071)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (39, 2139, 1071)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(272139, 1071, S27, 2, 2100), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 11822 186593 256833 696539 070776 372849 637221 705272 362399 854862 959404 778274 238904 525791 968063 310518 527285 436669 080570 941293 738737 226683 160748 914501 058048 523708 661055 184359 470550 222143 158732 561349 632775 565433 786505 194843 936135 865719 546536 736082 737529 196792 135036 146016 664019 985020 806369 958407 994918 815276 067845 511490 574193 358020 767377 844247 638413 613848 848845 711840 850805 728934 582732 359709 338242 499809 431239 472157 825781 760636 536177 450459 532216 059227 573228 779806 241589 619616 639046 580449 407984 097627 415126 842185 346685 351064 909225 976238 015934 054248 115371 513294 037325 638460 764861 086190 960529 336558 495557 120086 283303 268026 904824 472920 211323 699438 459704 473049 407055 352462 238522 933767 993143 964881 237388 690494 736760 087179 515783 802278 221217 883544 276303 893244 074568 199863 737328 007536 454447 004688 902299 853655 218452 375476 368382 926658 048441 919753 504019 276038 197637 977956 843203 512768 855180 173137 351052 774656 135328 468341 214921 067184 995325 408648 472785 308863 126118 499406 195324 790803 686902 256928 106267 415047 167838 788018 538117 575699 220899 495380 199352 259007 631369 657833 209445 476218 441434 265299 242144 698904 628070 767792 091739 519227 731831 836375 720015 677758 787798 389267 814680 680319 503417 102378 915513 401979 618274 499949 874052 557548 171925 260419 543232 754845 987698 299469 533016 468912 918614 356198 081579 308927 007291 216551 789128 498539 371982 149577 596456 809817 887519 921228 808822 158078 950903 086419 897614 467027 958823 406527 856137 517334 648622 617203 104547 806472 180068 929297 903422 770132 080353 519314 029863 053098 926542 957324 948792 608270 358393 067756 933352 781702 457707 832764 822380 062297 412188 359394 031961 463996 143804 394073 669126 873465 399192 784968 214999 567554 280954 269883 837578 120457 617894 091202 572840 707567 699905 264914 059583 676420 834517 203971 499940 055182 755494 491643 526557 321107 955433 809204 817330 833428 572213 856831 157317 946089 442524 659563 531982 726118 879600 436001 222317 706654 651643 746566 208488 552305 369507 602260 292033 276067 955158 959474 849062 239596 751512 628504 703394 056985 180923 585060 479089 875117 839917 596457 087145 807282 361303 911051 628262 908984 522422 174913 289911 493605 997949 264515 725704 899219 728843 951633 321123 414834 498492 205682 240400 938512 922003 151942 679891 196052 570563 690815 152663 440628 392575 631886 475894 324018 122297 451198 472060 656327 937521 698431 437227 594567 933497 226599 721932 979898 271604 342817 852728 732339 651376 025490 177588 658578 418225 343608 794756 265976 243372 986000 103407 445555 009181 347568 975988 136062 905053 927660 455229 987812 253153 439676 858651 424750 748985 437509 332628 342242 804975 159451 259441 578211 846330 087856 384668 412532 202325 333263 339228 302365 406556 320107 889058 374372 100784 818927 840198 994013 526709 861362 737129 946856 420955 973016 884136 267844 919164 892658 900124 720093 088781 865091 093816 465115 498070 275867 336729 710555 775764 721898 057947 864034 649041 809318 017609 367897 969098 671236 193597 025508 028739 434751 478176 970445 532477 852021 496805 378966 896750 594396 960615 275296 471066 713252 197982 417802 829277 855543 561879 183867 280032 550814 128352 110872 736139 581633 685082 455862 082962 162647 767111 117163 306231 258062 067721 484459 678655 977506 335615 995194 476919 695371 330551 209730 382204 349944 857927 323403 495628 748004 655745 340588 697207 717326 531609 / 191 > 272139 [i]
- extracting embedded OOA [i] would yield OOA(272139, 1071, S27, 2, 2100), but