Best Known (198, s)-Sequences in Base 4
(198, 199)-Sequence over F4 — Constructive and digital
Digital (198, 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
(198, 257)-Sequence over F4 — Digital
Digital (198, 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
(198, 610)-Sequence in Base 4 — Upper bound on s
There is no (198, 611)-sequence in base 4, because
- net from sequence [i] would yield (198, m, 612)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (198, 3054, 612)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43054, 612, S4, 5, 2856), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 610969 652746 549118 987003 054977 380972 794234 473625 145963 613725 872066 717729 341662 422413 545081 827506 101456 418864 078051 919978 816817 721175 978674 745703 608400 315058 309472 630180 517222 405442 318478 728501 664166 786702 137310 674903 210508 723645 472008 261264 269507 285620 586511 191850 066237 259242 495645 110491 718622 732145 276101 402406 386050 325933 788082 417393 417444 894879 752019 205768 015975 043399 429095 753317 816387 832667 208101 467997 378777 904153 673633 677076 098774 426550 165782 896312 031748 481771 394235 916413 410557 015320 150236 130705 600527 804685 639518 363956 198994 575695 621169 069522 986631 508783 153692 500499 647725 123321 681572 836049 871885 645306 049493 947905 540153 268006 511040 789689 671453 308700 772887 827055 540248 756675 914142 958372 355485 817463 132161 400545 488868 793110 458713 486520 321975 771815 325705 005663 250259 577050 100105 570101 671680 432371 953759 365720 358940 185281 771138 482685 861509 160268 833329 929687 050171 734385 094909 105098 821379 584824 532255 407719 422961 511784 083927 059767 558051 190854 235313 619533 299102 969355 490074 437734 630560 193418 627153 560278 933379 696464 083866 569473 494121 524408 722734 205072 610692 176767 790237 580490 484414 180995 839146 577198 500601 436197 335453 184027 869375 127108 359900 561315 108596 800329 074744 070271 157526 482396 801241 341548 548469 502114 712381 385126 508278 971844 691536 109386 832391 900936 008329 908424 931105 617474 137922 608295 598232 555658 138773 946368 066883 127678 110200 379312 577386 999238 824019 850774 547563 681209 854242 475479 271100 128586 659700 681947 024272 333682 534292 801992 098346 943209 677754 521306 684534 241915 705401 715953 383441 986124 628669 011077 297425 442839 072655 960036 562403 563055 949606 147562 097218 274414 894962 200723 476502 655938 752346 268223 496978 226227 472491 646325 644072 949812 958220 218734 316548 765937 897354 432153 997152 806060 285110 216143 451475 438879 243754 349774 785818 525681 265344 894645 810215 984194 875445 322360 888218 670564 131183 663935 640324 889807 457417 116303 850186 907246 919680 / 2857 > 43054 [i]
- extracting embedded OOA [i] would yield OOA(43054, 612, S4, 5, 2856), but
- m-reduction [i] would yield (198, 3054, 612)-net in base 4, but