Best Known (25, s)-Sequences in Base 25
(25, 199)-Sequence over F25 — Constructive and digital
Digital (25, 199)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 25 and N(F) ≥ 200, using
(25, 650)-Sequence in Base 25 — Upper bound on s
There is no (25, 651)-sequence in base 25, because
- net from sequence [i] would yield (25, m, 652)-net in base 25 for arbitrarily large m, but
- m-reduction [i] would yield (25, 1301, 652)-net in base 25, but
- extracting embedded OOA [i] would yield OOA(251301, 652, S25, 2, 1276), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 10101 410404 359298 409053 691323 049640 622633 019088 813045 298761 680330 372662 193799 146791 119014 689172 262350 642470 778577 430188 767040 257077 665687 696797 468856 709430 945305 595853 868201 521819 486549 675168 801417 048473 387073 908737 639726 061464 486716 417862 092086 835667 386232 639279 442293 352186 526395 105166 658345 617673 118924 635485 125873 566685 947062 422365 795039 238763 937186 821442 633631 646027 621551 429615 303571 836187 941843 687849 836228 723014 706957 617530 788657 078721 791226 108361 305736 941607 779712 440588 346870 989082 511962 932691 582593 212484 499692 809470 851090 551127 519644 630974 980044 106936 477185 192562 745710 729283 477719 134818 296699 140307 403120 520459 091922 943698 195449 444292 291339 458014 115482 454948 057807 768208 136443 938673 333536 567725 982436 032118 800401 992542 576411 469435 249105 593915 140524 417220 968823 474629 133439 660788 900283 994524 069926 333412 892155 161777 271408 368952 784402 155095 927956 469271 639880 071679 380719 870934 462846 598533 862972 113665 333357 666208 042755 741973 198537 025983 702771 496196 455627 864959 989703 484031 198930 363776 977111 004043 397232 980124 788769 652644 628699 489214 012649 445255 047765 585813 284463 547012 209714 507778 354160 732079 894455 230975 897028 306557 664713 374637 529623 994578 740028 764295 476042 921363 670323 080071 387644 142441 023391 162466 752211 121732 791873 256796 519196 874389 085036 866791 518309 618521 925853 794093 038654 502024 107225 324495 005218 369122 430912 941329 639715 938635 719830 086476 333889 801567 043253 669360 217425 861381 144964 726912 359183 139495 310377 473286 924235 084226 575435 885669 780263 201963 122122 415797 292345 112268 094464 451292 641907 220603 599289 868955 023451 265941 752203 881677 573060 606940 011730 084914 726851 867848 766937 132385 567904 774977 169872 537762 366643 732766 849932 989764 894252 306046 037352 679242 321695 196914 785879 718224 527202 066801 862040 905152 177478 633559 574306 805128 383916 974459 378925 365804 180656 333353 236398 138463 858487 057223 101146 519184 112548 828125 / 1277 > 251301 [i]
- extracting embedded OOA [i] would yield OOA(251301, 652, S25, 2, 1276), but
- m-reduction [i] would yield (25, 1301, 652)-net in base 25, but