Best Known (65, s)-Sequences in Base 3
(65, 47)-Sequence over F3 — Constructive and digital
Digital (65, 47)-sequence over F3, using
- t-expansion [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
(65, 63)-Sequence over F3 — Digital
Digital (65, 63)-sequence over F3, using
- t-expansion [i] based on digital (49, 63)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 49 and N(F) ≥ 64, using
(65, 141)-Sequence in Base 3 — Upper bound on s
There is no (65, 142)-sequence in base 3, because
- net from sequence [i] would yield (65, m, 143)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (65, 709, 143)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3709, 143, S3, 5, 644), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 55697 694223 247399 057873 566876 394479 526803 726642 453830 601096 126492 105166 928327 485924 287608 433636 451139 692634 899876 442045 985218 197351 359103 714395 427872 288166 234889 946924 066853 950306 568952 125295 993289 728644 753050 587642 797416 375940 887252 294110 538867 325238 347426 399210 453681 957198 884187 787399 569868 168069 937870 776181 065026 282407 109516 348705 593119 / 215 > 3709 [i]
- extracting embedded OOA [i] would yield OOA(3709, 143, S3, 5, 644), but
- m-reduction [i] would yield (65, 709, 143)-net in base 3, but