Best Known (120, s)-Sequences in Base 16
(120, 255)-Sequence over F16 — Constructive and digital
Digital (120, 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
(120, 257)-Sequence in Base 16 — Constructive
(120, 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
(120, 512)-Sequence over F16 — Digital
Digital (120, 512)-sequence over F16, using
- t-expansion [i] based on digital (118, 512)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 118 and N(F) ≥ 513, using
(120, 1845)-Sequence in Base 16 — Upper bound on s
There is no (120, 1846)-sequence in base 16, because
- net from sequence [i] would yield (120, m, 1847)-net in base 16 for arbitrarily large m, but
- m-reduction [i] would yield (120, 5537, 1847)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(165537, 1847, S16, 3, 5417), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 6131 006983 135664 283019 086612 183377 234532 760435 298356 318385 955619 458865 943936 925228 466527 827498 704056 361177 388798 000775 695552 835783 871721 092315 847846 664278 127583 103341 848526 343747 219825 592497 682345 948498 506082 646970 605068 983977 878936 327991 339044 468218 429552 925243 074820 885231 453064 234047 460816 290746 991741 786201 056764 730715 226535 270824 137314 070809 979535 618728 396459 092619 322333 778232 185110 850046 891233 068626 383438 371807 109590 500595 591845 356016 327538 035396 315150 988377 663953 273959 258116 798238 956960 062129 138062 596586 048373 414188 127543 929808 798256 030139 577643 050260 879714 032903 535420 448692 469285 322177 451718 344040 125111 905916 646961 582147 121153 074661 745459 152896 018207 721911 532050 033215 446002 398239 729036 468786 988335 654320 543777 817404 049701 585830 239754 744282 352749 632404 639964 764977 008353 302726 768317 312322 767093 426671 382282 969385 016813 949477 213744 681039 696816 410927 814848 902332 383375 438689 946532 992018 917466 030448 633432 520961 151947 422609 167767 660118 363836 539644 092252 051875 476987 267605 871249 294563 972391 276547 194072 392277 935149 991839 013664 852099 593253 470091 987618 712826 471606 186053 226654 422718 177494 705476 690900 990657 010471 443171 643075 976201 562467 319655 205648 929228 192832 767670 140427 025881 991232 636408 178255 866914 510473 025767 879265 773089 675698 966753 079273 568759 256250 999648 240366 371365 979852 682817 037149 877975 070882 328916 011484 421927 883104 013284 712628 269834 563293 399531 677083 806172 836244 585717 177580 124167 485837 114466 389452 757084 820176 215778 176479 946297 064730 251558 572682 378413 262650 340509 204925 461527 941957 316518 685802 034245 276604 778538 974001 364295 753530 049422 125897 440740 792334 196501 439805 389073 072494 848300 675827 315428 829945 782899 236376 760085 142892 176483 398822 900169 308263 990634 428640 603699 573881 868680 961299 379989 631154 443375 123442 516427 819896 683991 785259 443513 539744 048134 294333 312587 426171 251931 597017 726986 868902 888169 105539 937598 604894 482374 004905 880358 510596 914307 438001 715025 367304 466086 610790 805272 649359 481711 451710 502314 851017 004350 304464 761783 172226 813625 039299 449081 184866 744305 209804 422051 311941 545341 542486 546757 740701 655914 475773 459796 605944 251817 862666 603738 650389 847133 684344 824729 870435 948120 587607 387232 821389 754136 700773 566308 413769 491393 723433 534671 533496 133819 599582 919007 322862 054677 338231 280840 228309 083078 854609 565307 834748 989986 217844 321503 697676 983567 596735 768263 144916 565755 909903 899794 258116 146839 151791 931912 011152 172359 695059 468946 936498 473178 705030 561325 278783 481700 545228 907483 178204 473883 484906 226320 990527 551683 049352 886313 384449 444220 853954 467373 355508 464825 197087 276396 332126 409905 465166 914843 469726 922445 129358 097596 163714 074479 683798 967945 200285 119666 115242 516630 067631 823159 485445 496885 266859 226150 459873 835931 725184 749179 531014 530782 278249 936364 900552 914391 678393 922373 654999 439193 444312 735933 376219 961368 129799 829430 328886 602568 243712 215850 460807 739103 229680 844911 714183 279394 351873 030964 354437 056920 318931 105204 996097 461459 765032 826565 025460 203867 993061 409994 372434 611438 173815 195544 320747 649741 169855 676335 699099 201092 494552 156312 921460 771594 779420 574872 362594 069505 751520 761969 308311 812189 654165 254777 718035 423220 631288 658855 128757 673158 341421 156920 034208 113208 707915 559045 874009 850189 246829 134416 408508 834563 849141 152264 238224 272828 926011 808983 072927 482349 690052 585893 717225 590635 460300 564096 395421 873732 273031 801297 772043 085874 801747 513602 632996 167351 830527 000065 778811 859712 573990 365333 295330 489560 990149 449023 861637 596030 986937 998847 327023 799035 434853 881748 424936 144043 428204 748042 757097 044751 285948 817367 484277 805042 560660 482518 287602 582621 532124 254031 148031 301678 207799 467017 527308 579603 049744 229170 778336 959027 578802 824550 480363 205827 937601 813519 688035 970635 093511 247752 510020 358280 589505 633313 325333 804622 100919 116792 229852 966060 489552 460208 791217 032371 493895 326535 694815 552231 324652 432048 234421 744547 908205 810057 520794 783860 427757 183922 357634 480596 341738 424521 918510 971914 490705 157069 689915 166199 229525 115685 235086 485889 372469 893478 790295 009396 201929 921576 214566 222490 901831 860131 098756 395868 107780 564488 884842 417923 526078 600661 779323 009988 790358 650882 630039 014588 348198 651528 241940 365200 054417 283878 515953 788106 835270 191546 845089 761617 302534 285742 307219 402885 810809 754457 236437 545829 775374 502680 302379 773303 568083 395809 845605 517923 770055 413170 666901 736468 776188 609844 214471 548703 061987 039730 704838 432968 028704 924831 835294 416234 465460 808325 765470 158427 079655 170466 518469 432197 382591 908137 512442 492748 140493 560371 659667 889163 727137 039370 859584 323298 077534 656672 850309 148871 326286 052540 489431 036874 239786 316390 655992 776429 398312 687023 225425 044423 667893 123596 277243 897279 027670 943938 279845 232062 870651 893717 661736 720124 973453 139796 998301 093633 543553 627511 819038 285031 716572 710586 474972 125369 278157 812991 882454 646607 472504 158670 755047 871233 211545 443435 788323 125722 944260 609313 216741 731033 362585 370655 217784 804518 549680 850013 941862 865249 123186 753345 105781 395022 268171 472138 960456 999066 925376 486510 607553 743760 929858 949541 083083 779026 410919 214532 588660 521741 623055 846991 507151 761789 240651 695483 059346 184839 382741 833169 855849 747397 117886 075929 734293 499542 124072 936638 277154 744581 257104 202718 748504 653105 273018 774178 252231 362703 319803 881203 507232 978547 027498 798313 227744 490628 269788 174214 372702 053456 102906 977572 084499 435232 654562 707223 041081 969329 833125 369780 442719 112963 360004 899110 084434 194417 085951 751472 013977 296603 976585 549555 945575 268387 711515 651992 090404 310291 618683 531774 492181 604782 009086 097093 929686 374655 665634 220156 760602 687180 195031 152449 412829 055148 131109 823232 228620 482318 233074 551312 233431 793638 173746 631153 421018 083696 492201 137601 771493 893157 556237 193277 608981 675198 099572 575134 526674 041064 364143 161654 283702 330748 857966 643207 284793 087699 457565 913040 255445 936364 183305 711684 340000 952679 647258 767287 160700 834880 097465 484990 850095 288160 479774 689852 541255 253412 948672 956998 800499 869056 838809 457221 531851 834579 908127 758750 899508 394254 375303 159431 316444 352303 620159 298468 580429 598885 056895 823669 160033 315939 600503 050394 930665 644263 867941 314763 643162 699182 634747 475830 783002 167458 452108 545336 669030 087147 258631 393434 317776 758701 561714 281014 735392 991261 007566 294565 324418 685123 381374 566673 967282 757961 249414 296014 340224 309988 838927 813273 780648 969730 160122 885726 940183 290293 532457 979126 369776 327516 512563 459623 595660 779018 306099 928436 520921 486266 385583 608145 692359 868672 418244 256793 427808 972869 487781 962630 168106 344241 946702 764707 767723 292039 571072 266920 077623 253801 220436 712029 788530 112704 335908 015589 681265 978487 626244 853275 918161 676659 143645 443839 134409 253546 088371 428650 869963 114102 415919 425297 151319 280286 499137 156160 706650 325048 131630 860071 673094 190183 370747 132097 563996 004126 421287 687481 732396 081083 834258 447919 293096 647925 179459 293215 248131 042557 438551 220732 634114 517201 918664 000019 129547 823857 771432 902656 / 301 > 165537 [i]
- extracting embedded OOA [i] would yield OOA(165537, 1847, S16, 3, 5417), but
- m-reduction [i] would yield (120, 5537, 1847)-net in base 16, but