Best Known (54, s)-Sequences in Base 5
(54, 81)-Sequence over F5 — Constructive and digital
Digital (54, 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
(54, 103)-Sequence over F5 — Digital
Digital (54, 103)-sequence over F5, using
- t-expansion [i] based on 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
(54, 232)-Sequence in Base 5 — Upper bound on s
There is no (54, 233)-sequence in base 5, because
- net from sequence [i] would yield (54, m, 234)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (54, 931, 234)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5931, 234, S5, 4, 877), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 349822 518516 286249 024652 533430 581375 769868 347225 492043 723821 786951 307193 926490 700232 606037 071937 648302 617805 733546 809818 158774 506776 168722 477451 332651 717986 118560 796453 106663 555212 277864 532537 911678 845657 411337 815031 922647 228736 086612 855265 370386 672439 181626 621170 832748 418355 495595 590531 929716 691820 824068 982673 739644 122653 341085 140959 568172 762797 424735 768001 124863 642963 464706 623543 822548 334565 715441 904575 852177 094443 196632 023709 221830 032967 656181 485638 613981 074246 650630 262483 385020 227509 823650 662319 372252 242859 490750 126120 007934 027225 249035 829928 059525 742503 625002 330306 849893 293563 341269 127526 006292 244558 325277 292709 643006 674014 031887 054443 359375 / 439 > 5931 [i]
- extracting embedded OOA [i] would yield OOA(5931, 234, S5, 4, 877), but
- m-reduction [i] would yield (54, 931, 234)-net in base 5, but