Best Known (55, s)-Sequences in Base 27
(55, 113)-Sequence over F27 — Constructive and digital
Digital (55, 113)-sequence over F27, using
- t-expansion [i] based on digital (23, 113)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 23 and N(F) ≥ 114, using
(55, 324)-Sequence over F27 — Digital
Digital (55, 324)-sequence over F27, using
- t-expansion [i] based on digital (48, 324)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 48 and N(F) ≥ 325, using
(55, 1486)-Sequence in Base 27 — Upper bound on s
There is no (55, 1487)-sequence in base 27, because
- net from sequence [i] would yield (55, m, 1488)-net in base 27 for arbitrarily large m, but
- m-reduction [i] would yield (55, 2973, 1488)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(272973, 1488, S27, 2, 2918), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 27799 458271 399378 314865 346882 875944 186514 916248 357821 972517 249229 249446 786668 498308 009100 801633 756204 955705 513127 846479 560584 090573 239768 046424 722529 522853 390390 990223 781459 556963 064683 843208 632827 060301 908664 789440 427540 777674 234533 424025 598552 542679 149474 308462 112112 633298 183167 062415 147174 761171 277028 500400 315871 001866 419467 213678 035361 623717 805542 932073 716654 525393 232367 751914 053568 362198 913674 503340 481944 917826 398172 532816 070566 098717 183471 277323 440067 797103 253252 457254 548503 574673 973244 456061 067127 666147 851996 360009 900254 974310 005444 265031 355580 335578 040596 554479 500432 954731 540827 730403 752062 451894 557463 942505 511372 284753 646609 090750 372498 118670 331034 563802 318457 188384 215019 762728 499465 944140 780199 186125 254945 905622 775235 846658 059347 072574 648316 643041 263600 651535 440658 724553 995727 241367 007316 014874 613674 419523 463549 221071 764135 117075 483117 000668 337294 508166 226746 959684 835156 881396 819049 729187 274492 526787 970615 465820 738563 646675 560543 964988 248941 886821 121766 134839 018074 007854 734007 451276 631190 300830 435412 849248 981945 805775 399745 387612 735878 393908 323260 159112 149406 315446 827484 182721 575601 943938 936243 723658 519345 181633 307136 820457 815725 067663 715404 331555 617849 996454 599494 797196 359456 684449 941576 476727 238456 252108 421714 327044 661207 634631 224355 941401 352492 650210 888975 340629 146228 675821 927178 481549 032563 910006 601856 188225 625548 780916 804036 055129 852529 116704 961057 773433 590408 151120 469257 397657 275780 108443 227692 984859 087063 307532 770775 174785 243384 056318 602805 941074 308722 262907 427354 880089 672890 924956 074416 146657 393538 092754 286809 629724 093975 759830 328557 226802 183658 641734 532951 332209 078345 938849 355859 086172 872853 420986 497004 732158 336609 055681 457170 573738 369658 022455 045404 976670 471212 351312 175156 913792 396151 221311 680814 737263 688069 754989 362778 101744 968950 575682 352981 616137 226871 776384 407375 289095 333592 668631 143343 939241 350477 367806 567565 369016 877647 524950 124960 035670 668470 515944 859970 404032 151019 098539 726934 462188 212557 833042 636082 418245 247235 761446 320878 522097 299203 431896 845532 376321 960747 140104 381214 876241 881635 203482 978868 224500 335942 190846 756415 185747 272898 247009 962721 457705 265359 073623 008682 405558 535185 700648 584483 399999 276784 652650 331318 449607 053736 783804 087849 793486 809112 546220 353386 816654 945741 374652 817644 650891 693855 333935 785069 437436 423501 470501 479155 520626 559301 439987 066306 426392 244863 611688 858219 595793 918840 744258 037123 296083 866468 049767 403520 300210 073738 908848 765057 232358 777976 825557 578381 720849 713305 570255 570644 508595 301630 404884 609867 803384 199733 817501 825558 997594 946043 465427 486752 158490 657251 568459 985602 553724 534360 416171 587694 682431 883032 329882 372809 752790 218214 033724 614959 450472 391155 757092 714221 543072 097607 759052 716479 288571 790728 201440 200500 218451 646324 181626 112796 686638 087442 660034 177827 089664 112036 291668 373951 665111 274267 091201 482267 369634 489653 693291 069406 354315 815902 044715 651234 192892 825723 318320 470753 505683 901907 810190 518874 854147 074476 151778 100794 796318 639122 094516 546743 714254 632589 944280 806319 012485 965475 414787 048311 100629 246342 203885 033242 868331 808647 165485 761809 118309 313436 725569 364047 563763 014421 390982 333162 391481 769323 692469 646584 452098 343122 429968 639233 667146 458999 350497 903522 011894 553501 464643 836468 793256 230814 775633 696924 580533 395108 080568 578175 688826 955979 101939 166263 162051 079925 735025 001237 315588 698286 751282 386453 887149 213418 118181 550094 497390 120419 546750 059540 764590 297701 688264 209511 005513 668421 013458 594794 587806 281035 907925 877808 701505 474077 489811 184372 426320 682870 675929 006292 476213 406013 945007 111214 632617 540990 563278 024011 940358 752215 756936 709682 889758 611479 693234 184967 287410 691810 525069 947532 202432 936370 466279 339587 812594 275063 704012 347477 347974 397389 245205 329527 020565 177784 664837 969380 029934 107187 498577 477756 564662 583654 009100 728178 661903 556006 804371 658540 911149 705193 270765 531247 829086 904040 527828 947041 575723 875870 565966 934325 327253 846269 449092 930708 964496 602384 428709 957650 454685 947890 183460 668179 165509 586227 514857 020791 915836 181325 020705 581140 410520 399320 921711 581277 852340 715045 895512 096279 088935 165436 515344 652679 705536 791425 100292 547764 203627 698744 212938 229552 092465 026624 389499 197441 311903 850234 753767 963440 247352 619933 369230 521628 663806 015388 057885 605574 859628 568543 965071 978398 170998 791121 871353 644611 101656 483446 687979 236957 946472 870862 319533 / 973 > 272973 [i]
- extracting embedded OOA [i] would yield OOA(272973, 1488, S27, 2, 2918), but
- m-reduction [i] would yield (55, 2973, 1488)-net in base 27, but