Best Known (53, s)-Sequences in Base 5
(53, 81)-Sequence over F5 — Constructive and digital
Digital (53, 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
(53, 103)-Sequence over F5 — Digital
Digital (53, 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
(53, 228)-Sequence in Base 5 — Upper bound on s
There is no (53, 229)-sequence in base 5, because
- net from sequence [i] would yield (53, m, 230)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (53, 686, 230)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5686, 230, S5, 3, 633), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 101 229323 722084 670282 530575 465907 570362 135861 996977 141439 458094 073266 607065 526839 895013 865315 058008 971812 610799 791621 950554 592918 606856 624316 744169 840979 409782 546481 370777 803603 397222 563849 579087 660193 944844 380983 570301 266274 427412 356430 645287 921884 346355 734499 216023 872344 602503 133905 873279 233105 122563 904736 350029 544854 490569 687137 420702 598146 448674 063544 510893 837918 095009 932937 755377 159129 269030 415680 677611 246876 224564 390466 720502 817607 636736 330078 974788 193590 939044 952392 578125 / 317 > 5686 [i]
- extracting embedded OOA [i] would yield OOA(5686, 230, S5, 3, 633), but
- m-reduction [i] would yield (53, 686, 230)-net in base 5, but