Best Known (124, s)-Sequences in Base 16
(124, 255)-Sequence over F16 — Constructive and digital
Digital (124, 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
(124, 257)-Sequence in Base 16 — Constructive
(124, 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
(124, 532)-Sequence over F16 — Digital
Digital (124, 532)-sequence over F16, using
- t-expansion [i] based on digital (123, 532)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 123 and N(F) ≥ 533, using
(124, 1905)-Sequence in Base 16 — Upper bound on s
There is no (124, 1906)-sequence in base 16, because
- net from sequence [i] would yield (124, m, 1907)-net in base 16 for arbitrarily large m, but
- m-reduction [i] would yield (124, 5717, 1907)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(165717, 1907, S16, 3, 5593), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 301470 522658 328206 913685 942296 617301 431265 468653 489772 363864 772129 238837 803754 103876 055261 664452 921356 426401 386605 792225 541006 250842 207892 763375 192057 297785 455719 358456 112870 594266 297072 369529 340800 021487 014703 654990 473193 884369 635498 255051 105946 411284 399182 617613 684395 709631 455302 998915 310549 467521 187986 200202 299745 728084 483290 876494 851672 315041 650301 231398 344774 996278 699593 357168 715009 423636 916009 775474 938801 213709 884269 011632 157395 623282 065623 051099 878617 104051 684242 574774 032472 385117 808177 128277 272551 232514 652750 992225 186822 011584 250105 828448 435095 909873 446000 034092 412207 686959 802267 686375 953851 992252 290310 988381 057880 105063 368693 754581 372980 015985 662664 974354 915489 767577 087446 738843 086059 311452 028796 733426 796170 611018 641886 455534 549485 049332 805496 443655 026284 550562 022576 979292 843311 723894 706269 773400 267516 922210 214745 446115 256497 398086 707166 900050 084152 684924 662618 864140 787483 055433 740438 907987 988094 965507 120422 070902 699662 817284 758016 346424 052964 290373 825276 772912 504806 717819 108474 353227 563659 894927 785368 303714 969338 223107 628680 559338 276203 856274 796272 215137 114849 147764 403370 566018 761467 771101 946018 219506 652256 507044 161358 336271 685762 241539 091213 086655 879222 459299 803927 820325 413898 133922 203010 274931 994540 599918 410139 113096 477451 169053 796965 659950 129061 932600 580409 158141 588958 128069 266413 929940 590243 149021 535320 495111 407591 614456 062302 519535 785527 976618 076706 633010 638663 914291 143645 352771 190404 764463 055543 551116 727302 017768 455714 035909 671902 454036 902711 689218 776201 202261 727982 385737 987341 495362 100149 562949 350118 625325 292004 348068 115706 076606 281834 853499 196060 858684 606079 314494 489929 838621 187066 729622 923105 539799 266281 024381 533541 318397 038245 277284 291451 737572 276442 793195 872521 992722 066422 115530 702849 099230 072484 950190 660791 693464 280804 936261 224887 092368 375233 690654 581624 073433 937738 104297 412413 866709 378091 821528 690766 661572 786833 511513 584847 801489 755804 362189 105666 221524 536021 549732 467373 822132 079710 118219 707100 707332 089374 523831 218952 728150 850474 299673 991208 460269 532899 796508 874002 901295 151272 307246 865642 071521 008727 875590 327362 357254 867230 560746 880295 832406 103124 084441 560965 015460 346878 975898 764871 458921 442720 254026 761297 314320 971572 511830 562055 111511 188024 411605 255811 485024 974344 404777 696065 257718 372750 874922 819261 379987 311532 209762 647420 713479 841768 618388 269458 359666 626180 379290 201327 790179 059502 109549 113070 849626 394664 316248 563760 157993 271910 488999 884145 982892 662925 568408 288634 370712 015112 477858 715446 738052 589150 405009 243064 496876 413687 495552 224683 939596 936841 100879 577347 201814 499904 375373 878461 610673 174130 905077 265612 390928 620943 692170 981785 342879 676041 956354 106636 904770 091735 854187 154826 805684 157348 323135 613091 678448 375410 550792 088731 028529 880165 209236 726155 590057 676356 748394 382353 410156 289849 533218 826103 674962 674142 188498 655535 782458 512320 564742 593470 214383 863366 356650 549759 934806 183722 035111 418489 175262 571844 734939 931394 878309 342155 417530 044719 054220 651763 299212 024648 508393 868988 340504 834027 703142 547112 407463 109086 255013 369883 694385 920345 507286 553551 739712 689702 777015 978036 547523 838342 315267 582436 446584 613724 927218 085272 703886 097125 314904 763445 206146 096743 506018 337182 560692 099735 639210 850262 538594 407929 237750 679529 953889 387136 205612 169190 631054 071560 999473 923512 400224 350379 505752 505358 150152 911416 286321 508184 550593 271731 880130 831882 349276 701611 839296 223649 217432 527371 681848 840473 894646 322714 555621 575187 040210 062542 573053 918189 064916 197373 151956 666371 013323 058266 360029 251864 292585 368129 248543 467607 524697 893358 241567 646575 328628 308157 558581 466817 049795 058333 666546 782080 504322 787156 542449 498120 826756 118040 422161 809567 652363 063036 198728 544348 818984 513551 462879 234801 217759 319743 974476 033277 680074 851070 058079 689332 258446 175544 361483 613175 365705 820185 178683 741861 094749 708301 757857 519016 726303 958135 854490 099790 209922 281346 754188 553349 802251 546589 172592 106370 194547 280641 080525 369169 536966 738743 791225 145017 278067 174000 093653 763477 163696 771554 870166 472993 681805 896634 648720 912581 741896 441719 716189 105438 091206 774452 192707 109434 362361 752473 005948 351035 759067 067219 661554 852781 133189 610997 794003 052906 263701 573977 105972 326721 042375 452751 392559 279439 457035 468986 827148 259194 426400 964495 831918 515806 515253 711258 133316 659799 990918 854631 365264 251135 566365 543732 391247 905963 789713 867570 600822 543895 322131 754069 035210 381253 159857 983919 637399 452477 090902 146177 746910 102947 247638 970353 650886 004959 517108 263108 455318 481503 984035 814972 910763 672847 459632 578390 226460 770991 232025 151870 699497 731327 764018 267340 369003 753896 866037 075030 323174 775558 402752 639955 606671 689599 835840 325308 429811 938393 174193 412164 339214 040840 045794 237028 203576 390023 744013 059522 240386 825193 706607 557948 764191 633511 690268 390392 500822 238816 966212 219927 954950 172346 097732 256137 174520 206712 680541 031226 339673 020220 809428 178026 389829 717076 795841 189539 922320 404182 422576 873265 271339 542810 514680 489878 340525 440412 914618 609201 417671 207813 861170 390703 691610 301228 697437 724508 452442 617398 710376 368027 680605 528125 796762 471079 726997 113422 380533 193657 474390 729059 112309 057138 373337 824313 085955 931896 350483 833525 313587 500966 684926 660363 114318 731802 103360 931877 843236 753905 434561 198789 365907 715694 387614 262797 362803 880030 444157 554909 715063 542730 993732 582264 121774 138488 848083 963907 372440 812984 228291 507453 923729 067946 244423 961579 433582 239861 690107 854272 689821 864906 847632 836853 298577 984255 072368 460480 207070 959456 579429 081244 860643 096288 796530 919713 156760 804717 317413 665641 724422 631807 801944 794945 293121 437758 096603 628007 018974 162439 400216 630758 692301 630577 388702 688921 607275 092105 012708 396560 688744 797381 459636 440280 835122 915434 544378 029475 444666 721363 444938 834167 259965 142651 993951 960438 892274 364227 267686 515571 029815 513833 656916 890321 115430 872150 184578 921021 911345 848271 033317 928824 270517 861466 004462 987347 933011 480348 421979 791280 802665 367648 481608 296205 369500 148690 568523 397744 839470 781715 717877 399280 347603 190889 798894 411994 152843 286152 091175 368773 593614 308636 408980 095990 517900 584551 158152 984619 545664 793626 739351 218842 491189 692579 677349 390274 440130 943440 621904 671156 196456 659078 234390 394640 564846 353513 101173 001583 551367 863101 452650 114839 329366 455982 524757 914912 913171 167031 615916 409406 844338 591494 999531 910090 945312 538614 548733 495704 695536 036578 863517 557015 019166 102101 620295 895381 170490 185875 578334 022324 758478 657233 931439 763132 947608 176754 287043 226825 870378 544667 675684 476808 570085 071562 800312 213971 104857 052697 041836 028918 908410 343129 271893 819834 468996 843233 772287 869745 443745 987648 491960 762910 252519 932586 536272 880995 599134 039265 488090 640204 692331 604470 115664 318192 794383 190269 801123 627639 526179 556818 008133 813908 876967 217776 860473 810625 384008 793148 538929 247068 980343 389756 620006 598086 102387 158613 013189 857252 680779 964796 545788 447249 925987 883387 774206 056443 821908 531220 173425 314272 445620 498753 854599 145574 359009 020745 201906 379899 924873 856944 339583 949650 366285 075596 376196 902864 175108 247173 909977 104343 025031 751464 415248 071845 866250 322851 371451 128125 325312 / 2797 > 165717 [i]
- extracting embedded OOA [i] would yield OOA(165717, 1907, S16, 3, 5593), but
- m-reduction [i] would yield (124, 5717, 1907)-net in base 16, but