Best Known (36, s)-Sequences in Base 32
(36, 119)-Sequence over F32 — Constructive and digital
Digital (36, 119)-sequence over F32, using
- t-expansion [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
(36, 272)-Sequence over F32 — Digital
Digital (36, 272)-sequence over F32, using
- t-expansion [i] based on digital (30, 272)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 30 and N(F) ≥ 273, using
(36, 1180)-Sequence in Base 32 — Upper bound on s
There is no (36, 1181)-sequence in base 32, because
- net from sequence [i] would yield (36, m, 1182)-net in base 32 for arbitrarily large m, but
- m-reduction [i] would yield (36, 2361, 1182)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(322361, 1182, S32, 2, 2325), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 68603 559478 797215 066732 775602 574326 693269 447911 179475 620046 677478 106408 912112 698891 547427 169838 420688 836126 533318 901130 954112 177676 447473 759900 864253 014392 327763 970811 986179 080898 740778 736981 394634 356623 516079 232331 001600 614152 827190 465844 499359 122384 741526 163644 476558 098894 184089 106992 121206 912472 755348 051441 476715 914974 237626 959641 732375 512803 808545 778898 707900 126656 084302 677453 293303 330855 375759 985206 332477 508206 684865 763521 886452 171025 015155 607151 809232 008134 090352 124151 590752 945449 144829 503651 886300 351766 251304 201497 493726 866613 544315 723569 211124 262555 358158 489616 806089 035531 110307 499711 478984 789356 415951 026200 097512 537591 984872 446567 059920 310231 073548 304102 313247 618195 065951 418586 347393 292057 753201 771360 746440 423315 863691 671565 984938 711468 116484 451350 204975 469791 545159 180720 970217 286874 693602 432177 014284 480864 789966 831346 123956 705241 372052 167996 501651 052407 504576 288486 227061 095231 648493 956062 086571 832697 722882 702091 713540 980209 930175 656327 297694 617637 791673 839556 953626 767207 743305 415456 012318 559435 297201 215550 661834 021696 779259 520523 926022 145792 675774 111159 649522 796641 408361 542474 510192 871125 417902 183521 160595 623020 531211 877264 478752 314765 769274 142465 717970 877986 123359 189687 840075 607756 315858 402478 802454 826117 395930 053072 051007 375593 223043 382718 058523 158462 303001 110984 584100 375489 891809 417324 144308 066613 079671 074241 531972 522266 964272 570657 335979 040904 591141 865539 664387 265405 692152 318531 804557 910764 457170 957358 535581 526623 257923 678250 577347 331304 524290 621200 995587 393074 794878 082038 935317 907961 079015 979361 031001 831189 008817 253776 180668 943211 959221 718557 084631 850602 886186 129187 139324 232248 920294 906490 384228 683080 691837 124656 209873 252766 070477 587035 548518 742942 950030 925788 285316 832204 593357 354104 797456 318623 557060 799075 735703 293913 144410 349334 736879 435819 026231 423461 838931 210379 996371 997890 632819 901457 040598 914821 628358 065225 356855 542859 487704 495164 706327 770485 255411 572632 576142 292595 010066 849959 047867 492695 941239 737561 474056 728198 254953 998878 929209 998376 575523 871435 074995 253229 521461 899342 518165 760153 061803 040256 035418 426736 911959 491832 842273 447754 091005 425544 542035 107212 442474 967633 024201 356910 946896 937251 323164 053231 396732 130222 544626 238427 409196 631039 988976 548368 433148 973720 306451 352289 067845 043679 203014 014219 282070 705885 400825 390308 851908 227746 548484 111158 229021 869493 011612 694256 091087 316198 705886 515497 357333 613666 832105 811817 922582 174032 315138 161398 502352 528891 717597 613211 690739 235312 543100 377193 893704 075291 807982 455744 283059 818577 746001 777639 106630 659314 931292 814711 873338 821242 669935 131710 206077 908589 963699 877937 704607 140081 522448 091003 489130 944062 078566 701009 123320 245379 067310 803446 976641 641929 657486 560719 759232 385115 999937 663697 506955 566340 415391 938805 735805 239270 800974 435338 386910 634135 344218 768300 763995 954486 880959 552620 914100 485162 564863 733224 148428 188669 613082 900351 792655 529512 625571 568685 139154 608154 685148 789074 885128 559522 707846 362323 868445 422116 645109 531994 739066 955199 793686 650577 746564 533133 680718 416432 827155 010879 146606 929762 364725 988254 646092 139153 524076 498396 669929 638339 884338 498864 418768 857227 334098 856283 207289 119693 579654 822671 564607 778260 585320 135666 582885 402060 838884 312410 903789 149954 571808 488719 107255 178855 850969 419188 516651 926916 178207 355790 819519 739186 823402 580882 408151 194142 147144 172796 293012 097647 723682 961849 320834 148586 548580 797936 180633 621377 175229 304400 332776 574406 872457 844138 980944 358416 251681 232888 473814 273678 225430 181098 260302 849026 881387 063834 526808 660519 941801 250036 367282 164053 692660 927279 580466 447688 917070 963562 191470 450474 576558 227319 147357 100602 032128 / 1163 > 322361 [i]
- extracting embedded OOA [i] would yield OOA(322361, 1182, S32, 2, 2325), but
- m-reduction [i] would yield (36, 2361, 1182)-net in base 32, but