Best Known (5, s)-Sequences in Base 49
(5, 54)-Sequence over F49 — Constructive and digital
Digital (5, 54)-sequence over F49, using
(5, 91)-Sequence over F49 — Digital
Digital (5, 91)-sequence over F49, using
- t-expansion [i] based on digital (3, 91)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 3 and N(F) ≥ 92, using
(5, 299)-Sequence in Base 49 — Upper bound on s
There is no (5, 300)-sequence in base 49, because
- net from sequence [i] would yield (5, m, 301)-net in base 49 for arbitrarily large m, but
- m-reduction [i] would yield (5, 299, 301)-net in base 49, but
- extracting embedded OOA [i] would yield OA(49299, 301, S49, 294), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 8015 341832 617176 840463 238704 698494 935036 281874 838137 960397 720884 896142 562446 431279 765914 688803 267693 009281 452911 243865 381628 895620 283123 326996 619646 023291 340804 911156 773614 596647 492611 081203 991958 425119 031338 304396 989462 361408 046757 553845 252375 659711 607555 350845 012220 985389 698350 570920 272209 776388 425146 775466 377893 946997 192700 703810 750319 099796 238594 013333 045170 203797 787444 184466 482909 571715 643952 756591 501679 014605 852868 500459 574819 056295 818024 263132 381318 894379 805860 486940 688647 938949 337157 928978 520007 / 295 > 49299 [i]
- extracting embedded OOA [i] would yield OA(49299, 301, S49, 294), but
- m-reduction [i] would yield (5, 299, 301)-net in base 49, but