Best Known (114, s)-Sequences in Base 16
(114, 255)-Sequence over F16 — Constructive and digital
Digital (114, 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
(114, 257)-Sequence in Base 16 — Constructive
(114, 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
(114, 339)-Sequence over F16 — Digital
Digital (114, 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
(114, 1755)-Sequence in Base 16 — Upper bound on s
There is no (114, 1756)-sequence in base 16, because
- net from sequence [i] would yield (114, m, 1757)-net in base 16 for arbitrarily large m, but
- m-reduction [i] would yield (114, 5267, 1757)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(165267, 1757, S16, 3, 5153), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1440 040389 772461 363939 948002 284318 831299 087390 135103 198118 024259 600408 708129 663569 186166 610838 001003 231380 886196 364654 534988 765903 954961 647534 188913 428954 013919 651580 448040 998959 136133 335203 390180 362578 428017 687828 550656 139264 398574 268943 852650 706395 545399 175884 463430 955143 147268 680610 008056 781615 547762 533062 078243 081408 793993 939149 079584 145070 310899 886240 862523 814059 731299 071796 832085 186968 104133 317994 968279 962949 379593 717616 944407 299125 663129 320432 439922 139218 663835 530986 915843 356863 284887 693886 407965 055149 530850 502135 188177 512052 265697 883057 570817 652492 112538 169379 280623 490700 876720 576076 708236 102115 113713 618333 702770 217887 531933 484028 261675 716593 661639 273938 031289 645239 305914 624381 791926 454417 746994 805383 973072 896109 420370 489901 955879 213740 099603 380605 957809 094472 632853 539162 416664 685469 520066 210220 049616 332607 273934 996559 368091 944725 086833 084453 221309 922950 385264 973924 660811 357741 298418 422488 093707 819733 698412 482922 107214 947937 563925 255182 499782 259086 857998 555360 474540 103955 639829 042355 700258 326759 049383 010825 480978 603475 509656 773618 177883 528912 747836 848700 671500 047948 502605 255804 640462 469541 644160 931215 194992 882173 583894 555154 160681 405637 928502 808820 216936 672466 575972 864815 567722 057740 328313 631537 756295 817993 201760 343780 952051 583513 324732 945638 682150 442261 424746 431469 581500 553132 287090 140797 925483 062927 960071 869218 610867 461937 785537 158487 714161 683626 811381 761218 143167 364973 406282 376870 102269 772625 492497 162427 262737 950798 584238 503751 807687 126706 055387 962867 056024 578897 259023 687967 688193 119602 841501 201967 883002 116152 162345 790224 605599 418454 389704 497476 929075 488396 934649 793311 374690 835242 019282 375370 193783 006166 061947 265843 660861 125607 046436 056356 715056 269821 937924 704141 123769 676510 824639 926484 345519 458820 361444 226229 672429 967809 721743 375828 317925 576187 392798 565271 239200 159308 209114 438050 116661 497318 399331 416667 981501 104707 623126 709659 540341 006047 689201 799748 015144 990313 224892 922948 257795 833705 836639 586747 090804 276704 066185 423630 692489 388104 633574 650203 369061 504887 682736 054047 566475 981249 870870 622114 375787 917529 176702 891968 490117 228248 342688 528393 630819 483316 773702 047545 613779 804691 362584 825535 187856 025684 979375 081563 225096 244724 051014 579740 339370 972695 386983 197215 877756 903703 044072 737485 296391 583803 838218 805261 018432 256972 903608 923124 402384 096754 746593 443184 414850 054317 254169 889970 874861 381413 591051 096927 831288 439392 699737 799619 025740 718406 661823 256375 183780 726643 606848 387863 119618 675898 808134 995228 305965 528689 217333 567207 993080 641239 007883 781467 821410 939552 038284 030559 473518 642750 286361 617649 182960 638103 522391 580799 190304 919316 436497 775059 819863 136166 460639 294004 075837 299857 172502 762597 280616 208873 125509 704644 020788 287725 213984 148423 661946 191251 120757 645435 929743 187573 600344 834094 873494 073044 158459 219716 334921 035672 562937 874129 222446 777669 211503 054115 645685 883055 993250 126336 637743 352391 674269 310654 467555 352998 912375 663281 296610 177187 985063 087536 624204 667253 539614 430477 926212 349258 915880 666204 463147 238152 579848 692032 505119 005429 020760 446542 777400 000987 929576 945706 220520 774232 025144 318460 411782 679086 590526 308270 472444 352012 009716 808292 939913 657792 134552 271937 221858 574633 379906 071960 421422 157154 485457 882625 763951 055374 779867 424217 908905 739433 359687 007179 393036 470642 255595 450691 340734 844944 352292 087327 874757 567817 689956 070272 042185 939713 802591 819415 564634 418421 124080 873526 102772 485917 392295 271512 517477 840152 818767 576909 181512 742968 014455 013004 359769 439694 699296 332350 946393 703898 516383 816110 098313 525995 300553 887088 320192 969287 218686 550241 039434 056002 624405 068674 042781 606619 742406 682038 621050 121248 523893 659704 799254 219312 308370 616920 561083 995990 131836 946870 809816 431345 005248 963419 530631 817785 927855 642622 017337 933857 007998 551962 355426 375376 020589 146507 880012 343846 423748 325650 749308 153999 668676 143234 410388 638667 540120 044795 940114 605970 167308 531653 096206 868872 341222 289882 998015 703781 065342 501237 838632 959214 000827 101561 734144 791938 393253 295182 353334 355755 167230 981487 420586 631543 748241 575427 308534 949339 528056 413088 493949 631676 474897 278777 931317 516557 135460 070924 568881 441696 388913 484522 925489 484339 593455 394254 502231 661244 664946 552877 073183 632004 253333 334430 965200 395670 026447 692016 086012 977982 676205 507000 451943 803020 712197 061184 739696 940833 775276 496718 019877 009961 477487 949009 940847 080455 042772 384098 237402 472301 259306 389682 620972 321960 574046 999602 503822 033949 535824 327762 994993 073651 709533 757073 747940 530251 415847 159013 739524 702136 887495 783102 906808 222625 593360 347308 376624 266453 279928 667806 937998 458756 208421 356193 103629 682910 355902 273460 375491 869177 927533 661537 546948 714847 930113 816854 040630 813593 530398 053331 880898 180245 861736 615712 022364 982817 994835 118999 510259 994052 575477 849987 790071 452933 686886 168829 109363 510227 759599 730543 468249 095796 287534 222959 022333 241100 690940 094200 884931 475140 142366 422180 288971 827611 578049 798994 861105 680122 353942 644833 992161 575654 272655 649815 619944 633979 572723 031946 632906 352907 812629 032695 087010 354544 562134 787356 841505 470821 821038 777614 038197 348323 986957 754198 157851 259740 099169 484765 533703 264529 321097 713092 278715 696507 713064 528926 235490 356529 457481 418182 154441 967626 073065 061039 851285 867964 055526 541528 599163 373268 143242 325692 825922 452062 899065 327995 230067 382024 531308 559696 127139 966545 146164 578996 748231 534528 711252 713983 021032 807636 133461 641884 733700 541952 836589 067667 338282 089892 578212 109017 990334 476456 729497 552969 410296 133319 291137 617255 219821 634337 005302 840286 367486 372431 231197 413501 262098 664567 223950 300464 251154 148201 341230 473114 289639 894005 116534 105451 869968 767989 760157 780771 892762 994902 002543 442770 578833 769197 181837 036048 073258 856960 214518 827611 251184 591141 517674 697107 092362 008597 540281 047935 331756 299496 243013 301307 690969 898638 693968 346914 046899 885076 549326 069812 565433 314798 110729 125888 238796 996209 140866 704716 621336 278875 780064 864290 597548 362303 442592 317353 511484 399019 989219 414384 692268 398744 010403 420909 354137 590909 830963 311223 398633 890659 518198 881905 877479 820788 595950 477906 531012 414493 401076 655165 263115 635320 057079 477610 804876 839180 734191 954210 617317 668217 548088 693662 585718 367806 489426 250035 355628 769846 793206 818364 645710 929163 697309 798049 075448 520149 502941 653770 143357 172182 710110 562647 001319 990696 420898 238826 665761 702217 463112 377726 911148 734811 792473 783441 427943 933802 970143 881296 781757 372361 250053 288507 624426 290704 979543 187559 992218 041695 455912 591184 233044 918670 860645 404871 227368 886319 120267 914071 224315 019264 / 859 > 165267 [i]
- extracting embedded OOA [i] would yield OOA(165267, 1757, S16, 3, 5153), but
- m-reduction [i] would yield (114, 5267, 1757)-net in base 16, but