Best Known (51, s)-Sequences in Base 5
(51, 81)-Sequence over F5 — Constructive and digital
Digital (51, 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
(51, 103)-Sequence over F5 — Digital
Digital (51, 103)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 51 and N(F) ≥ 104, using
(51, 220)-Sequence in Base 5 — Upper bound on s
There is no (51, 221)-sequence in base 5, because
- net from sequence [i] would yield (51, m, 222)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (51, 662, 222)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5662, 222, S5, 3, 611), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 287 412438 858657 281843 180944 663910 021292 434882 442526 851367 934354 451856 163316 617990 982718 682388 338445 531544 906338 960073 246196 199647 121756 605217 254813 781396 450834 111520 430348 742917 807829 296793 230438 312893 731692 445040 371774 628045 468057 041137 925771 743447 582524 902705 415226 074496 923829 560005 743944 885281 675562 648295 643730 308991 696083 594549 634106 368761 628606 376223 443595 122923 531895 259037 916949 159414 758506 143675 225667 888947 526039 909730 055654 790703 556500 375270 843505 859375 / 51 > 5662 [i]
- extracting embedded OOA [i] would yield OOA(5662, 222, S5, 3, 611), but
- m-reduction [i] would yield (51, 662, 222)-net in base 5, but