Best Known (132, s)-Sequences in Base 5
(132, 112)-Sequence over F5 — Constructive and digital
Digital (132, 112)-sequence over F5, using
- base reduction for sequences [i] based on digital (10, 112)-sequence over F25, using
- s-reduction based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- s-reduction based on digital (10, 125)-sequence over F25, using
(132, 209)-Sequence over F5 — Digital
Digital (132, 209)-sequence over F5, using
- t-expansion [i] based on digital (127, 209)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 127 and N(F) ≥ 210, using
(132, 546)-Sequence in Base 5 — Upper bound on s
There is no (132, 547)-sequence in base 5, because
- net from sequence [i] would yield (132, m, 548)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (132, 2187, 548)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(52187, 548, S5, 4, 2055), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 13 542514 904140 454359 902623 843243 349029 231735 362923 649520 384935 443284 844109 242201 333054 172461 797078 285972 881443 759844 615506 730247 119022 592423 413823 379203 301875 422740 786644 603855 201531 551759 398012 109114 909930 210794 760376 272349 909519 256935 766543 567280 835822 703334 522242 218854 924648 623187 112976 787186 706911 375051 076628 829700 621100 835719 402267 844075 370922 904247 602781 185006 213279 948146 629851 704332 391623 009579 020067 575207 218923 052088 372617 221156 159184 393862 153623 357710 760795 345203 877789 680460 435446 982517 759518 887747 894843 563423 575942 456947 029820 267841 746111 675350 343107 150188 945476 994228 584044 011929 447503 462604 904718 944455 493505 146023 816744 133665 205399 494046 600239 666703 589259 434225 028403 182826 633336 021374 823593 365546 466842 357386 284311 783104 249104 718866 363233 930382 928495 368580 118507 304431 427332 308885 119646 675326 703001 618726 799475 296199 742584 071547 076675 822635 421495 104367 681055 239615 285997 577315 751350 691600 825362 460399 811284 843014 541882 405747 816070 497012 011705 217767 828528 104845 340461 698337 522168 464466 959958 053131 093710 739057 581869 368715 618711 248762 967922 015740 501145 428034 938464 952252 900032 201432 172190 773517 061231 756810 050842 357309 762326 146360 718691 304336 172942 698569 898049 708351 508643 417509 742241 139495 653991 837680 365470 972684 017568 669023 376894 392822 826481 713132 385604 130085 966260 984989 594522 352980 239600 352802 072874 105945 436228 458355 094651 871883 375490 184122 308018 963741 955854 967429 131118 325327 258921 394625 514165 272885 340897 278749 240957 884819 884469 991857 469360 956612 353131 477967 147053 460827 965665 203009 848482 906818 389892 578125 / 257 > 52187 [i]
- extracting embedded OOA [i] would yield OOA(52187, 548, S5, 4, 2055), but
- m-reduction [i] would yield (132, 2187, 548)-net in base 5, but