Best Known (93, s)-Sequences in Base 5
(93, 81)-Sequence over F5 — Constructive and digital
Digital (93, 81)-sequence over F5, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
(93, 149)-Sequence over F5 — Digital
Digital (93, 149)-sequence over F5, using
- t-expansion [i] based on digital (76, 149)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 76 and N(F) ≥ 150, using
(93, 389)-Sequence in Base 5 — Upper bound on s
There is no (93, 390)-sequence in base 5, because
- net from sequence [i] would yield (93, m, 391)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (93, 1559, 391)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51559, 391, S5, 4, 1466), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 9 174463 428343 932901 733617 971745 942782 529589 477135 966045 373071 795239 463615 998773 927195 630554 393058 044705 725812 774244 341800 256131 243409 636153 632190 245885 833428 698141 152596 710783 485103 069828 929629 961773 022517 147506 017163 253729 917602 539277 620500 788671 815363 838107 903741 979079 607396 134011 570724 340873 469285 135428 488839 622931 801848 358435 874185 913377 139774 499693 961362 985142 820009 156839 556981 053691 878013 110109 387890 632246 547310 514163 896964 974908 507448 141740 895698 848161 386052 346547 347659 934865 866972 152562 378182 642334 693001 407566 940617 751357 774601 611657 907201 756637 633944 007967 412414 813973 068132 650961 063714 511993 400222 797385 148993 165876 661257 073412 863246 030287 602110 985076 182486 381530 871406 683128 863515 271712 508709 192688 030608 494449 628028 027367 417662 843267 779287 922256 570879 846016 927785 830774 413670 812010 503061 208809 103082 618503 579665 202026 497760 532255 202573 374265 424806 522218 491005 813005 101606 648792 067697 398759 468846 508620 141657 670730 601461 563459 056043 551813 218608 502596 023181 724830 968603 228575 326221 920354 504495 807814 334079 697482 970333 168299 221019 887398 735626 060641 834556 008689 105510 711669 921875 / 1467 > 51559 [i]
- extracting embedded OOA [i] would yield OOA(51559, 391, S5, 4, 1466), but
- m-reduction [i] would yield (93, 1559, 391)-net in base 5, but