Best Known (39, s)-Sequences in Base 5
(39, 77)-Sequence over F5 — Constructive and digital
Digital (39, 77)-sequence over F5, using
- t-expansion [i] based on digital (38, 77)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 38 and N(F) ≥ 78, using
(39, 171)-Sequence in Base 5 — Upper bound on s
There is no (39, 172)-sequence in base 5, because
- net from sequence [i] would yield (39, m, 173)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (39, 515, 173)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5515, 173, S5, 3, 476), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 526 745314 141014 601244 924425 404569 702264 713302 131153 736907 925982 282693 410945 577105 286117 351634 530213 612406 756979 943424 665147 273921 725287 000396 835391 089940 981335 864043 457513 934785 598787 745066 990445 239662 902032 638980 307379 094029 063315 352237 881874 602606 174765 436260 615358 958190 177870 016486 898124 005162 999994 599192 161423 683992 450828 217357 639005 058445 036411 285400 390625 / 477 > 5515 [i]
- extracting embedded OOA [i] would yield OOA(5515, 173, S5, 3, 476), but
- m-reduction [i] would yield (39, 515, 173)-net in base 5, but