Best Known (27, 27+∞, s)-Nets in Base 64
(27, 27+∞, 177)-Net over F64 — Constructive and digital
Digital (27, m, 177)-net over F64 for arbitrarily large m, using
- net from sequence [i] based on digital (27, 176)-sequence over F64, using
- t-expansion [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- t-expansion [i] based on digital (7, 176)-sequence over F64, using
(27, 27+∞, 425)-Net over F64 — Digital
Digital (27, m, 425)-net over F64 for arbitrarily large m, using
- net from sequence [i] based on digital (27, 424)-sequence over F64, using
- t-expansion [i] based on digital (26, 424)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 26 and N(F) ≥ 425, using
- t-expansion [i] based on digital (26, 424)-sequence over F64, using
(27, 27+∞, 1820)-Net in Base 64 — Upper bound on s
There is no (27, m, 1821)-net in base 64 for arbitrarily large m, because
- m-reduction [i] would yield (27, 1819, 1821)-net in base 64, but
- extracting embedded OOA [i] would yield OA(641819, 1821, S64, 1792), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5 128031 078587 781419 436060 366781 071212 846059 268199 022800 985369 801703 773729 059263 758729 279267 286985 026907 558500 843420 331662 032311 129026 894181 390980 813689 377988 904756 680413 272785 050987 407200 056750 850352 295893 460789 363728 016322 795004 380483 785484 317988 630341 064614 771582 358400 136269 684688 018234 635306 852379 171559 459330 863730 156389 997247 953914 912915 362751 901832 221793 293846 543364 308095 630267 423850 908411 581749 562788 478061 337655 905769 067689 650134 271851 322326 821909 975998 039417 307838 180249 999806 658902 741429 872324 938474 720278 214271 610829 889656 867542 896299 601807 305579 198645 837222 370533 488972 952691 576426 037284 669321 727188 162868 713517 949518 945087 009380 804683 571537 951159 866464 930840 296387 323440 175377 654516 978297 134610 504012 222086 461014 587325 967632 269726 327800 360198 971568 806126 604620 914424 129410 100880 544407 361406 507635 582463 834239 116834 758461 025829 995661 575862 104154 333883 498289 709057 459241 057824 465980 274541 355528 859912 767691 537112 840382 392004 908680 681207 964603 781853 559582 869280 688247 393617 445111 443613 514342 279111 764363 101138 752385 967785 811243 538669 368221 915106 095801 901425 551156 465982 060489 426826 703584 619757 365788 011526 188701 550949 895772 209993 449302 795690 062648 007120 653235 944196 871064 681169 144795 490315 406929 357890 632028 323480 644367 675623 966413 243841 144020 773054 688893 549262 271361 058784 486469 214948 643374 903667 592554 531486 510066 657117 115587 276427 806504 721481 498623 545096 791753 830522 403336 239764 730468 411252 347216 778315 634566 396196 201470 865967 782464 437158 152865 800377 208854 134063 654050 943263 797237 573248 683308 843762 672868 174760 238720 964941 422923 886109 157473 921487 970685 765463 299043 220276 815722 557732 591318 034590 554928 879947 548613 703221 765008 984219 020993 537243 060082 500425 858097 621999 131286 285798 171559 329194 817985 832793 730005 389772 074399 810973 176229 889568 790844 361924 173010 546479 767488 805742 897859 224028 215951 648312 493173 785879 512266 126949 118522 454599 687955 974043 376855 197790 762561 555116 467645 992321 597191 724226 957843 784908 762588 293366 006614 106389 893595 786503 806170 502173 863427 120350 996631 453454 845734 506640 448951 954691 989471 305967 215197 325385 537092 394860 918783 011153 551989 788401 635670 681559 861129 293918 143597 896244 386999 934839 996273 256041 563716 204855 537478 618548 630256 973503 697907 898421 214672 551868 172436 803089 177808 453957 477084 734284 886959 587741 917315 200397 891093 402634 881177 615744 670953 223278 603374 560335 508085 400434 024785 501034 896694 411945 690401 991058 925712 019879 823733 468291 325603 970560 885692 562164 471973 609633 505631 239465 338347 378355 616979 573835 243058 362939 787227 086699 325094 765142 185132 579275 129954 251947 185214 455440 160389 030104 681368 714876 331641 035118 786174 675813 148725 349084 468913 885630 334924 879453 572105 008982 069340 028542 727625 241195 906965 115534 189975 900526 364498 476582 913372 227526 041694 333554 083382 938894 147261 689314 375801 131888 226755 731843 347560 116061 120553 744947 021225 793696 334502 639256 906182 036002 850137 074676 212376 274882 475092 199478 223675 010196 807014 772253 231315 777584 259155 756701 877993 646590 971518 076310 357124 360238 161277 546186 350679 183587 493334 545196 162363 478282 006045 825662 216724 279831 250184 244601 742450 994379 472244 571816 735111 684765 054089 953110 632765 798827 296741 174343 054197 212568 269310 625173 487888 206123 209023 539089 938830 624201 152274 014481 929500 307362 135535 477546 662195 500061 004949 970021 627822 671614 846918 805112 268046 008460 290412 197941 431411 908950 318463 321646 959589 064704 / 1793 > 641819 [i]
- extracting embedded OOA [i] would yield OA(641819, 1821, S64, 1792), but