Best Known (214, s)-Sequences in Base 4
(214, 199)-Sequence over F4 — Constructive and digital
Digital (214, 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
(214, 257)-Sequence over F4 — Digital
Digital (214, 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
(214, 658)-Sequence in Base 4 — Upper bound on s
There is no (214, 659)-sequence in base 4, because
- net from sequence [i] would yield (214, m, 660)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (214, 3294, 660)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43294, 660, S4, 5, 3080), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 643638 175269 892718 889651 223375 833761 570778 312011 179944 939894 979984 441243 501431 551213 046232 932484 314468 145795 294055 605804 220217 095696 256578 675946 229118 048320 551883 943500 740871 683108 769814 010047 800081 231825 174153 337107 788015 361271 419337 582815 876092 248432 871629 211773 376206 181215 376557 187534 229565 816443 034269 431092 882656 369146 577600 606776 483194 347254 725010 922664 147879 654162 772424 600329 005535 305150 686975 464612 061070 369434 950902 336555 947067 405900 121418 094911 381084 863892 788377 506296 157900 610633 475066 359906 657629 880705 778961 489916 957156 032916 630335 488154 647558 382696 514704 020623 351529 152612 939242 156307 885444 226049 940962 809992 883539 031327 134658 781648 213300 370704 242876 210033 749252 059889 737050 626810 201723 491375 528565 490333 812538 670767 444759 118027 089550 754239 355293 306121 273306 585526 066497 495347 996576 030117 039957 672559 409081 280583 560502 672930 059772 002728 253086 619757 769697 338408 231655 830354 360633 507047 376006 795847 547995 011687 368079 858047 714514 710272 041890 212696 094851 476132 937960 422957 176991 237873 521035 533122 479388 258593 905280 118191 533510 500733 496925 531825 281198 235568 857831 213635 922501 899560 546905 659778 822589 561747 398944 107278 350485 644018 268649 015239 742154 538898 852161 902374 321463 116851 616007 871924 455299 530704 744120 739995 077466 147950 520544 172553 638832 245024 526611 004320 457514 618739 325218 823028 266643 914095 491521 626945 308964 239733 213800 888233 972567 888684 945659 699656 264757 788750 501503 795157 045086 771739 304534 844486 347814 204208 007344 758784 323112 314953 879208 460093 205911 778166 125545 151588 031469 160928 017322 719781 272742 913002 284106 641788 198819 766461 821875 457456 735917 482758 660909 869178 226408 666846 315958 262780 464773 247027 407030 724012 891084 900291 812065 549453 765417 273759 279366 575047 385532 390669 914114 243864 158517 809321 575397 884112 270354 551199 902735 578360 748950 134848 917252 802433 187014 846234 014495 939551 067482 649607 159679 105712 288464 297489 167551 743079 992393 423225 900705 067157 272407 143700 961930 982562 556948 027959 492234 605475 525606 381676 903973 536790 615030 711204 077682 661266 096120 657484 972032 / 1027 > 43294 [i]
- extracting embedded OOA [i] would yield OOA(43294, 660, S4, 5, 3080), but
- m-reduction [i] would yield (214, 3294, 660)-net in base 4, but