Best Known (117, s)-Sequences in Base 16
(117, 255)-Sequence over F16 — Constructive and digital
Digital (117, 255)-sequence over F16, using
- t-expansion [i] based on digital (75, 255)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 75 and N(F) ≥ 256, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 75 and N(F) ≥ 256, using
(117, 257)-Sequence in Base 16 — Constructive
(117, 257)-sequence in base 16, using
- t-expansion [i] based on (113, 257)-sequence in base 16, using
- base expansion [i] based on digital (226, 257)-sequence over F4, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 225 and N(F) ≥ 258, using
- T8 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 225 and N(F) ≥ 258, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
- base expansion [i] based on digital (226, 257)-sequence over F4, using
(117, 339)-Sequence over F16 — Digital
Digital (117, 339)-sequence over F16, using
- t-expansion [i] based on digital (101, 339)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 101 and N(F) ≥ 340, using
(117, 1800)-Sequence in Base 16 — Upper bound on s
There is no (117, 1801)-sequence in base 16, because
- net from sequence [i] would yield (117, m, 1802)-net in base 16 for arbitrarily large m, but
- m-reduction [i] would yield (117, 5402, 1802)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(165402, 1802, S16, 3, 5285), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5146 650044 995970 074959 155618 958368 800126 123577 616258 753134 957023 447515 086774 805847 776187 757637 270570 462146 942409 087286 639105 438465 652393 837058 652499 448022 763124 029625 262826 356082 411539 549253 938354 818887 608276 410132 440323 677623 972121 618409 574339 650893 958553 148209 469438 101606 767683 800671 714039 253196 819747 001053 439665 853436 974635 016375 963984 388577 452162 086986 400877 202762 280850 720259 795066 259029 011795 531055 904617 017710 760496 346980 308418 246275 896525 756950 189803 048019 113684 816589 444753 787348 606130 749462 302330 595733 298294 492802 219829 954359 497534 501306 996061 692369 504789 304143 008812 286481 708149 372708 521093 544896 245782 155720 360147 986132 550085 809331 962884 736980 593909 940352 721698 275723 260827 911089 038502 890157 214746 365263 315187 754882 751725 758243 264678 101872 322248 134355 548213 562820 688647 439096 811492 980394 118375 899361 461252 537827 429182 416010 476835 495242 608679 418443 354443 568348 548776 756424 573879 188966 032817 871410 298778 320957 654330 408876 723554 466411 828623 286562 476172 183165 131184 462960 765936 547468 916889 196982 652384 206999 162846 130587 160290 311133 021938 433663 682860 148139 481730 328299 952129 406394 079843 212579 794517 106288 778124 919412 919514 837157 599307 137297 291114 254311 367457 993569 377311 126001 148685 204019 064493 856267 568421 831887 406041 810368 192519 668007 988225 818161 937582 735600 878535 153567 169276 346888 663983 473698 600463 763739 302527 322170 562068 599659 093604 228665 940751 492245 041175 448670 639883 364885 878351 878217 130370 416893 852964 066977 918600 462659 500145 079131 408645 367968 690270 481822 591658 774202 029028 544352 801104 595935 025859 877796 417912 915117 794312 215308 389755 314041 428464 446412 468145 219058 819718 734210 634072 651059 189936 980057 602887 450635 171763 787945 769790 777281 209753 855780 576916 878494 924116 517903 965838 755790 482089 430906 563254 729386 981230 476487 870100 330418 518786 793005 400836 253811 861193 993702 053378 674674 003924 701148 483161 838597 221054 637212 531865 566930 814322 883806 592257 851946 424570 483131 241153 600702 795592 552437 227564 885764 839127 176832 823048 838144 058825 423459 338290 549276 801666 607713 185107 575524 114633 601743 535307 862469 629301 450330 571674 586136 058677 532174 793056 927797 529690 230726 139417 814414 970974 291969 253798 605707 419506 804841 319555 658450 667126 166327 979465 570870 180677 063737 370186 393915 205080 091793 039721 811461 859130 650025 068537 577251 147433 287162 553111 663411 925917 366084 019367 368294 647445 078201 694391 896831 583412 049155 407081 613974 563388 269359 408043 073773 484668 992533 011254 580414 195382 981020 204401 341802 746021 793957 641787 181019 766741 091286 723293 292722 010061 624675 218251 205944 608061 229136 315874 470590 118169 683936 347393 807386 695650 499176 443775 479060 394134 013759 149240 132114 681809 130870 719463 958805 094036 190554 163325 252053 861419 422886 844652 851770 011508 991648 597809 558113 829446 619348 575467 773659 143338 088561 468008 616825 469059 285641 138239 525133 312730 410446 376097 125223 042875 792444 815267 022678 175759 118602 979829 597898 461628 048687 020347 488018 152829 567978 612364 804749 312096 330703 031888 313842 891541 479208 899077 308602 052154 169589 734182 070305 684359 029989 659737 539714 609425 420591 717746 188174 431974 053109 054009 718635 454256 184034 870254 145123 275009 011710 697816 795650 947241 480852 654538 034694 072048 146344 511006 652005 834783 715501 455164 360824 902063 091267 677976 600545 185685 670773 375633 195299 227561 423823 523279 392076 578334 312693 298373 619686 860396 644413 945585 704435 145760 016321 805272 856245 922861 088915 504227 797429 760230 683300 028667 977293 561147 130776 750527 522761 216658 891566 267132 846590 616414 639597 828228 907885 078268 187172 941379 044985 187617 902181 761172 246047 544064 092249 482620 626973 165561 085803 863893 589302 427539 445957 813793 672364 385194 239593 891822 150614 426120 772895 643732 522449 320956 852856 431079 552452 519408 366743 831673 552763 804245 440631 182662 145362 277594 838975 984213 536598 177296 098047 304013 306762 529171 861712 619998 858524 363865 848430 092508 419047 384203 395821 248769 919368 798136 870333 815881 140533 893064 568981 434165 276626 670684 417891 614191 326201 935797 947272 126868 755501 977563 015398 066127 581419 407188 762538 548829 243307 886323 016183 749885 443614 619162 107241 737859 363041 092550 433554 630490 707704 249181 289193 334785 224318 534433 529625 493376 045311 115467 241373 088495 218493 725439 812490 797500 252435 713957 236759 977700 780502 150128 965387 583369 375979 644246 126554 122059 841911 614512 730598 312018 264426 402242 313612 873397 009502 164254 545584 456554 959415 870181 601338 364820 905902 270648 238084 314440 701442 789764 001090 378443 449807 352541 132429 156438 573978 642080 541530 343707 467377 688587 636422 011452 654627 248332 163493 165635 741326 142520 199902 124707 085864 033999 073264 069815 336663 498027 655567 641155 900571 881589 307053 988135 159025 699834 215241 502579 645643 954091 749073 251301 206376 931035 954958 318782 561583 892158 355009 013025 213227 724515 520734 626373 951761 529153 967675 088504 673262 295546 954965 685027 500172 578388 883909 348876 055635 510657 042101 969551 040507 546133 935987 127820 093802 418743 242229 855649 323356 122434 589441 619539 913350 797335 253060 482536 284260 459344 031000 541420 029258 238842 335193 616191 884761 463704 293424 100977 546809 077810 347715 184776 762813 871042 852672 739131 181900 998849 205848 699574 796513 200870 715102 709813 563537 997219 453847 087427 853164 198179 646911 492364 804575 833238 814765 146304 943245 022348 179863 887456 253063 911256 411797 519632 062710 585398 645164 386594 361934 599953 288319 676574 573113 192237 754335 363861 983130 124513 903613 404350 941473 605144 223357 086577 654049 534977 341734 847632 116972 114057 058944 602090 978195 724645 363114 953632 689149 985537 629030 915731 273154 354877 826566 998896 856583 846313 285224 765640 422053 763625 431137 093163 203692 712111 316373 695183 626104 355961 645352 535734 859633 757568 584226 826733 503443 818632 442119 255998 448173 434586 456236 293112 163444 652173 346275 976575 252751 908976 710245 786386 349324 803761 678943 569287 769741 277310 799516 696757 810238 884087 615579 970459 279708 923328 046687 579953 848620 047297 391821 141854 138339 039330 562366 098797 021651 236352 826355 264336 177152 099581 099174 358308 662764 295658 363519 924924 341709 373645 586879 145389 914154 529208 421640 029279 495290 937142 871389 499964 721396 389264 390307 821037 980692 968250 323983 732320 588304 685384 951809 557339 668536 720819 658515 679529 713122 556380 899689 766006 664644 009785 323032 226404 035125 694685 457406 493748 314957 949268 035816 063474 016467 099825 236294 640868 012858 049067 001420 863994 063056 694873 059394 512938 812199 447224 279787 755502 152923 795202 682541 274275 088661 376229 971122 041096 021871 193919 139510 534096 011743 892975 091065 755333 829289 765232 053031 378466 143256 114022 650471 456276 693108 653247 594631 215567 287352 515376 518511 205175 274438 534856 653359 312421 913228 808506 864748 713223 025526 292061 805914 712870 238356 364222 723285 704783 196574 036914 907729 225185 091140 723280 402544 605520 133915 985363 416009 241204 118228 155936 152983 839547 221531 579850 647229 904658 649176 866816 / 881 > 165402 [i]
- extracting embedded OOA [i] would yield OOA(165402, 1802, S16, 3, 5285), but
- m-reduction [i] would yield (117, 5402, 1802)-net in base 16, but