Best Known (50, s)-Sequences in Base 16
(50, 242)-Sequence over F16 — Constructive and digital
Digital (50, 242)-sequence over F16, using
- t-expansion [i] based on digital (48, 242)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 48 and N(F) ≥ 243, using
(50, 254)-Sequence over F16 — Digital
Digital (50, 254)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 50 and N(F) ≥ 255, using
(50, 787)-Sequence in Base 16 — Upper bound on s
There is no (50, 788)-sequence in base 16, because
- net from sequence [i] would yield (50, m, 789)-net in base 16 for arbitrarily large m, but
- m-reduction [i] would yield (50, 1575, 789)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(161575, 789, S16, 2, 1525), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2491 059172 424328 874525 686311 808897 902868 413214 911003 546755 116560 560243 735443 456935 002420 963845 228005 778373 877769 196607 108992 945658 672232 763142 951054 171492 054453 902721 708083 582692 677926 535370 429956 180478 982041 491113 573943 683930 336095 870942 115915 550298 086646 915158 554521 116567 834789 864137 162274 304387 499371 588471 915805 278647 001095 180951 277775 856847 629555 905494 380903 669426 630177 955200 861119 350765 319538 902783 321611 119945 679401 062410 540623 781178 009283 639962 397706 018127 239238 177903 495443 843852 596411 835359 138301 341711 532450 089138 888046 940453 779411 468759 623386 382521 218587 025587 639768 552477 389085 665502 677917 509618 351707 213163 118797 221482 241115 624382 795131 822877 027356 383258 024620 233061 450423 492903 771551 523328 000313 958966 988774 253485 015927 534032 859868 110801 712849 268674 856394 298151 018710 899311 350586 250655 197496 830136 065299 174956 418345 703238 470155 518149 007165 366835 338445 891341 552048 662547 899549 559409 168776 735189 424515 697228 150061 038875 897960 298587 909207 000568 644517 442096 525620 506630 882147 762912 449162 886731 569559 725790 183658 908660 149746 216207 690209 281146 920780 175361 351111 842190 048702 114526 541545 891773 208501 479336 939930 897400 019926 816123 309672 040582 770441 261478 473694 807067 618769 908632 825036 820116 278711 553965 107052 610678 757666 609553 222423 481307 272233 109209 465139 096980 907092 555873 260739 914228 558591 408671 194959 227738 489888 311568 428313 349813 867336 081485 116088 528968 216294 835339 425391 784713 703676 350304 243768 297623 584808 116545 011673 525671 099555 193781 148271 147751 183812 524382 865216 007685 995765 756998 517342 881552 059330 083572 452486 793046 098149 703133 559807 665291 161110 604410 292229 427362 696951 991613 228652 229821 704554 347971 299898 361871 195334 098639 944298 847565 469220 529452 499511 714356 992584 127354 243400 948866 689672 786496 025346 224919 069600 433208 752713 193391 780035 302939 368784 020179 498829 332492 533721 793995 896849 292327 089366 025020 012464 879114 723115 177131 362554 294304 915033 548270 401685 782454 886638 138119 159808 / 763 > 161575 [i]
- extracting embedded OOA [i] would yield OOA(161575, 789, S16, 2, 1525), but
- m-reduction [i] would yield (50, 1575, 789)-net in base 16, but