Best Known (77, 77+∞, s)-Nets in Base 27
(77, 77+∞, 324)-Net over F27 — Constructive and digital
Digital (77, m, 324)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (77, 323)-sequence over F27, using
- t-expansion [i] based on digital (72, 323)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 72 and N(F) ≥ 324, using
- F4 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 72 and N(F) ≥ 324, using
- t-expansion [i] based on digital (72, 323)-sequence over F27, using
(77, 77+∞, 325)-Net over F27 — Digital
Digital (77, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (77, 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
(77, 77+∞, 2062)-Net in Base 27 — Upper bound on s
There is no (77, m, 2063)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (77, 4123, 2063)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(274123, 2063, S27, 2, 4046), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5 070937 292524 290210 997919 586003 954863 523962 458526 546842 588169 321474 853608 776396 959393 772175 404148 573719 886712 054177 497634 764818 884108 937676 414104 074229 275656 633258 580328 038117 152954 171887 006086 546782 347487 858327 003150 233256 026055 270361 007123 622456 444516 230332 857255 407277 978605 042223 498099 998863 779015 992121 716189 505628 306122 679470 146999 243904 723348 002382 944463 269307 333295 962771 812201 069572 700402 030729 860734 619315 030995 062810 714519 750816 546459 771089 691627 388888 202058 552920 742118 259916 560357 417644 202776 415006 098086 429398 024972 261612 896700 813691 152849 630097 239045 179014 328248 678893 747099 405644 699561 985085 523437 993441 043519 783172 955411 658625 400868 012959 450809 461515 486997 005885 851183 447887 172733 197859 470297 600634 991948 554398 022429 317579 387148 339001 972742 207603 549339 606807 843837 574685 773310 839077 618280 896805 466665 074550 505255 612158 861999 350759 326129 451786 374418 562682 700529 914541 595100 061842 152596 877845 962960 004380 628476 004938 039736 678740 364918 605009 879943 835857 578187 028549 378921 272283 739493 702046 918659 721547 130659 409177 183490 797093 937239 895270 062160 708051 831011 297296 899002 813019 418703 009357 883405 635923 355472 881533 433102 381819 555353 739570 792667 594540 183646 532916 776734 363022 741277 547330 794863 783755 785529 218255 746247 573134 596672 973826 999136 518860 466293 573311 153016 695580 585731 384662 456211 213093 672500 035492 882664 052963 785806 601021 188710 782087 942259 041492 057091 138391 684543 942769 858489 732430 252594 796322 427790 998317 602132 591050 174777 331574 414910 208814 619698 114618 948567 961140 654276 018170 804770 533124 418444 602614 854710 947276 028245 614532 326668 274795 015866 489542 917491 895577 983042 546424 870757 816752 102442 476913 036513 790863 373087 402582 874332 810624 784619 675849 564090 671115 028227 166199 027171 535742 160778 987827 158337 307744 200525 383240 355705 879975 211418 474321 971607 853286 800915 092743 969576 188430 117106 516827 075865 750412 920415 508663 846443 826962 261575 050874 865264 117837 239325 137601 851622 306514 721261 849545 175029 047362 851355 818068 008225 979040 754442 681451 309260 913220 044031 996971 756610 599343 921587 823021 748371 955961 634923 309173 507396 814152 944640 093821 412226 628268 451609 827964 318347 578035 411272 336388 171323 363712 481483 539480 818615 918131 090472 261021 581841 494582 411405 419233 607515 267510 033189 278995 988000 442517 586260 868077 108960 149322 059540 292510 459563 993894 216208 432390 518577 380477 483040 321789 286562 321449 675368 343022 251323 273532 725250 518139 747127 009982 181357 330732 906838 439692 528839 099045 377628 032749 402159 216997 584445 121741 822687 053847 116590 819654 507993 837931 345847 104707 636312 458373 446112 409650 042083 757247 360926 062424 179900 090257 063185 630900 878161 077615 960810 201487 422142 845911 023565 194697 296827 534686 859956 949546 136521 912985 618469 620009 305592 461515 427622 911054 349406 719026 832861 444186 086686 710818 664788 859881 653900 587527 492386 523148 724138 174047 193924 408595 804102 013214 988674 265687 780070 084520 525874 697154 857721 882085 348251 597312 986029 882559 906982 997950 499959 988114 888515 736273 710360 909385 723710 843823 640189 878779 915023 064785 075448 231458 192137 810398 914127 272121 150581 224591 765535 482192 039925 699237 057103 055310 137654 839491 813676 978340 838307 366023 151542 435673 977551 139792 118394 564925 776569 600563 654280 868314 676171 237038 335899 858280 985046 316035 521693 466964 105095 368290 562669 783730 676995 600496 004312 940180 455425 600908 139355 495623 097372 424933 218092 355235 746333 915268 327284 601359 202676 945933 147531 346089 838730 320435 060696 296782 301374 655076 251113 833076 197151 951953 237926 358931 095760 743599 541350 567573 193005 960155 343705 980047 582284 543057 952341 975216 943545 789760 155010 419069 792838 996637 431949 398830 925628 599430 562771 101405 602694 348793 650672 492419 662674 383341 564704 877810 080993 715943 495006 120357 637450 628737 888644 473665 876888 321661 929318 270913 200549 060561 204698 978897 998848 210850 600994 895147 662537 944530 221774 431643 611247 716871 623101 474200 467912 813838 811866 462265 450776 117088 563781 110350 894413 279359 849355 094358 068697 785009 673959 875769 640319 342825 707514 468496 358131 818970 088507 564863 907725 759212 357749 734381 847822 979959 170426 030149 434752 735327 535829 900790 109523 727042 303417 851361 191398 194646 451775 373884 769554 616773 857428 259470 369019 229199 860069 586493 036868 824409 689328 775179 371825 051877 114551 648287 131964 226429 637069 756720 327291 823150 498358 188574 479040 136013 428365 527446 400783 682864 730939 847249 534749 829267 594443 309921 989501 175749 096117 644215 797958 558585 640637 577671 537591 187184 519235 842529 396348 079584 432252 491190 988396 259451 290437 256198 517560 129791 874454 527431 064230 397442 633989 743469 725685 730929 368470 390057 873257 706907 408885 650986 888527 198257 115322 888214 813962 753763 702440 907104 084956 310811 591971 994085 313108 954398 821581 971319 972709 407247 296446 149234 799288 746856 888341 539637 810367 539335 911052 142238 788964 449639 165625 181819 531374 794557 790840 298030 990216 075969 510050 010924 420960 117563 839219 469640 373446 015686 403461 839320 345598 246843 413604 597163 852632 276111 532405 781574 881835 527746 658901 454838 413621 755767 126733 754497 802671 876284 928502 233855 138307 385470 245971 417511 904491 034469 074010 671790 404288 760655 119312 247319 394980 841134 149275 264061 843791 400766 717340 472332 189012 792149 427581 912787 234113 832476 878856 312291 347617 472747 658140 324420 214769 905819 860635 273674 236847 215185 150076 636330 531871 280011 143733 333035 297565 998181 264955 806031 906507 235335 805356 545470 564537 223882 128933 219655 511240 086753 147797 366262 484043 517941 930966 045772 764709 173333 446688 338132 686834 880212 583971 736330 317776 506439 564863 444707 802208 228990 989807 701618 148501 070392 485479 856526 320328 381443 004609 613260 383581 614107 467188 413314 916795 649282 355042 744244 109130 548461 661879 255776 127885 859344 406029 394378 765042 934760 264662 447761 346333 653663 232894 559794 412182 683587 578879 570851 561240 056435 914831 336975 204368 419464 830505 825431 682578 304352 314270 527083 105314 479140 263732 502284 406539 593248 690354 132818 019308 074004 470302 953125 932826 122001 290439 053112 160247 904276 045717 307135 658696 323992 558398 959844 081677 604224 104021 259141 889813 412830 924974 312234 269169 859875 862994 131122 799316 650762 743898 003813 331550 547685 658604 469861 119012 571540 205328 545791 497438 683425 541631 / 1349 > 274123 [i]
- extracting embedded OOA [i] would yield OOA(274123, 2063, S27, 2, 4046), but