Best Known (106, s)-Sequences in Base 5
(106, 88)-Sequence over F5 — Constructive and digital
Digital (106, 88)-sequence over F5, using
- base reduction for sequences [i] based on digital (9, 88)-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
(106, 169)-Sequence over F5 — Digital
Digital (106, 169)-sequence over F5, using
- t-expansion [i] based on digital (103, 169)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 103 and N(F) ≥ 170, using
(106, 441)-Sequence in Base 5 — Upper bound on s
There is no (106, 442)-sequence in base 5, because
- net from sequence [i] would yield (106, m, 443)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (106, 1767, 443)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51767, 443, S5, 4, 1661), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 107 602087 563768 802874 677136 608947 478269 433696 747775 815383 182871 127504 156650 600168 851910 747193 434743 081397 406848 895902 925388 366960 542450 940705 991444 288717 412776 345521 741842 497237 043593 156855 467376 474481 873487 076321 742102 436917 271054 092265 416233 829460 472226 262037 642820 256914 036882 142835 511909 175938 664806 202789 671800 289898 895736 384954 294776 907813 127077 367362 950004 754817 674298 131718 171749 801664 136603 145496 106624 488655 022922 670017 189896 540586 199172 932553 393182 369416 733254 536389 225651 997487 342506 365666 054969 919768 477112 494103 081372 977281 543529 959321 061908 601997 483133 243287 125474 006201 109270 248848 476018 983892 205994 769330 491296 255212 086753 526551 994008 528320 765063 636857 285964 623223 296953 841408 539499 730274 593899 635319 133695 308896 643400 414196 393794 830790 681274 928002 280667 600384 754297 819829 335845 390215 798443 811046 050528 332282 005826 144268 692761 783813 691949 411604 278432 756004 889526 790575 299999 530938 372125 488441 527012 958339 727003 664969 859711 202441 130541 910295 559973 082469 486175 966898 110303 316201 718277 425692 031688 070983 211209 549050 126765 860548 501848 228099 276431 311795 867296 426988 838213 522906 474150 014764 280831 860391 384402 428512 121743 981094 853385 325280 060771 771212 486865 356964 166751 937220 733093 661969 963228 397517 696066 643111 407756 805419 921875 / 831 > 51767 [i]
- extracting embedded OOA [i] would yield OOA(51767, 443, S5, 4, 1661), but
- m-reduction [i] would yield (106, 1767, 443)-net in base 5, but