Best Known (113, s)-Sequences in Base 5
(113, 95)-Sequence over F5 — Constructive and digital
Digital (113, 95)-sequence over F5, using
- base reduction for sequences [i] based on digital (9, 95)-sequence over F25, using
- s-reduction based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- s-reduction based on digital (9, 103)-sequence over F25, using
(113, 179)-Sequence over F5 — Digital
Digital (113, 179)-sequence over F5, using
- t-expansion [i] based on digital (109, 179)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 109 and N(F) ≥ 180, using
(113, 470)-Sequence in Base 5 — Upper bound on s
There is no (113, 471)-sequence in base 5, because
- net from sequence [i] would yield (113, m, 472)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (113, 1883, 472)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51883, 472, S5, 4, 1770), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 366856 424009 927879 506603 178815 886319 129270 280018 589582 354188 414522 056980 563211 794198 964117 783730 322345 722716 178544 184947 646346 139814 346002 634122 342779 976852 485117 218230 601994 627278 836919 746756 439436 833727 466846 147278 684672 845036 293866 523185 985326 197148 234860 874418 711423 376666 815242 904505 695059 224230 406832 139452 626059 187876 880554 567344 463225 498091 709566 503218 214629 500063 086618 520857 830409 981705 600805 471358 348997 385525 824819 208062 399994 099771 270224 912697 337540 751705 180693 527839 245286 586062 763411 119919 149065 676200 262668 677395 341439 536870 062326 533807 999739 611238 519964 583932 475634 738371 373119 685308 470365 250828 831516 583518 329133 605707 237279 723504 216013 668692 574443 312711 873750 614554 828095 098082 311642 956728 773466 053896 166822 505215 361742 252931 531370 163193 942277 813386 721703 992691 442767 336931 561798 244746 869681 968640 453265 995289 679529 083890 980188 376752 397408 381234 939396 620395 125798 309328 184117 640097 155769 252032 996950 265609 354479 781497 648513 833893 602431 167368 871070 527588 004328 300738 400507 602127 791184 139004 133660 119062 822050 291344 712216 362505 149724 241242 731038 455413 486326 001859 274361 586010 409331 876206 523736 206256 800033 816208 182773 433397 331480 309828 832148 001747 254775 435788 689559 975200 930007 196603 541054 825834 795829 120056 899724 075133 630322 246379 920042 194986 406457 139238 533322 715685 169868 038428 830914 199352 264404 296875 / 1771 > 51883 [i]
- extracting embedded OOA [i] would yield OOA(51883, 472, S5, 4, 1770), but
- m-reduction [i] would yield (113, 1883, 472)-net in base 5, but