Best Known (197, s)-Sequences in Base 4
(197, 199)-Sequence over F4 — Constructive and digital
Digital (197, 199)-sequence over F4, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 from the 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) = 161 and N(F) ≥ 200, using
(197, 257)-Sequence over F4 — Digital
Digital (197, 257)-sequence over F4, using
- t-expansion [i] based on digital (191, 257)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 191 and N(F) ≥ 258, using
(197, 607)-Sequence in Base 4 — Upper bound on s
There is no (197, 608)-sequence in base 4, because
- net from sequence [i] would yield (197, m, 609)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (197, 3039, 609)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43039, 609, S4, 5, 2842), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1502 162078 287494 285586 777879 307307 505871 176654 752621 967943 872417 081119 328861 630054 692215 890624 063531 636146 746085 275948 482189 199534 092051 331369 777212 892384 907630 609563 504373 699693 404664 479736 806445 778838 066310 067620 327759 610968 429473 159224 269645 044945 242316 718427 360903 268168 700914 517221 874331 407229 769602 053652 648840 085168 972929 457684 887977 137819 450753 409061 053382 909141 924926 520045 249208 688021 137512 960568 008908 021399 285832 889342 725409 937391 236703 965265 340396 709085 435668 628580 340581 863516 144185 694824 210593 015009 636048 096455 642771 083210 397449 230963 862128 583565 253229 654533 686582 887597 753576 129423 223782 078743 249299 043893 121783 128500 068044 113322 746304 230862 687063 086444 026584 469224 020708 705967 364541 838554 503295 643879 609325 992987 404516 788804 259860 322638 824107 811183 883931 741201 066812 030917 730310 124998 159631 673836 372355 101280 409949 609844 292414 418967 509678 773800 357572 224393 135076 298282 193397 458732 606230 918874 257273 984983 443865 080200 577705 780575 382781 274618 577346 754893 934101 310528 383353 690910 717214 495253 668557 744303 760246 958008 374176 866955 895659 859930 919952 802220 502954 368290 539885 103387 482809 515419 938543 622653 565678 935252 773871 641900 658384 281643 143541 745174 892167 634446 188239 981808 822072 564398 701050 901945 903191 825780 641450 316163 511914 713473 816322 064788 908110 294189 868436 305933 548213 907746 246818 440498 597161 178147 702163 166034 675644 477274 422904 107090 875182 164852 809414 846529 903946 958973 331969 291795 828411 053797 864453 875693 644056 976194 102217 991677 788819 295947 045619 352621 427026 344246 069432 538219 214576 202533 428694 855567 807102 996746 021365 761990 033061 296573 622563 145377 031083 109682 737025 328571 710230 914701 198262 933827 633123 249317 125660 099147 973944 113657 492773 887379 725320 273770 426504 112296 005726 945799 404907 041814 586941 700611 769039 044167 556049 038904 224102 393659 313269 255512 074055 408568 886031 126135 654884 579903 255242 376716 041370 730496 / 2843 > 43039 [i]
- extracting embedded OOA [i] would yield OOA(43039, 609, S4, 5, 2842), but
- m-reduction [i] would yield (197, 3039, 609)-net in base 4, but