Best Known (7, s)-Sequences in Base 27
(7, 81)-Sequence over F27 — Constructive and digital
Digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
(7, 223)-Sequence in Base 27 — Upper bound on s
There is no (7, 224)-sequence in base 27, because
- net from sequence [i] would yield (7, m, 225)-net in base 27 for arbitrarily large m, but
- m-reduction [i] would yield (7, 223, 225)-net in base 27, but
- extracting embedded OOA [i] would yield OA(27223, 225, S27, 216), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3799 493282 830239 438492 224482 691690 909566 619472 854971 357390 219606 335900 386951 333682 126198 574578 485187 205013 112380 672962 324296 382818 471396 758867 711250 989008 236860 018335 444893 297349 120779 943212 574909 820372 429439 350519 300231 559090 380242 472844 168996 781328 574945 725848 543713 005874 816967 435615 187281 082638 861007 407109 672715 461769 / 217 > 27223 [i]
- extracting embedded OOA [i] would yield OA(27223, 225, S27, 216), but
- m-reduction [i] would yield (7, 223, 225)-net in base 27, but