Best Known (77, s)-Sequences in Base 3
(77, 51)-Sequence over F3 — Constructive and digital
Digital (77, 51)-sequence over F3, using
- base reduction for sequences [i] based on digital (13, 51)-sequence over F9, using
- s-reduction based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- s-reduction based on digital (13, 63)-sequence over F9, using
(77, 83)-Sequence over F3 — Digital
Digital (77, 83)-sequence over F3, using
- t-expansion [i] based on digital (71, 83)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 71 and N(F) ≥ 84, using
(77, 165)-Sequence in Base 3 — Upper bound on s
There is no (77, 166)-sequence in base 3, because
- net from sequence [i] would yield (77, m, 167)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (77, 829, 167)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3829, 167, S3, 5, 752), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 95 990108 485957 288904 598860 495980 114713 140508 312656 277183 323509 392425 769223 982023 100832 077881 345702 982528 762212 345950 136146 607470 700818 456075 380209 724546 032763 338621 218805 960621 295054 309539 357203 900014 623899 718344 426295 419190 909646 308296 698789 891735 947234 742531 623631 216636 352364 710057 148813 797509 826899 454896 203449 301960 213871 481402 909137 128430 818089 526466 986322 002599 178089 020566 464022 362369 180123 / 251 > 3829 [i]
- extracting embedded OOA [i] would yield OOA(3829, 167, S3, 5, 752), but
- m-reduction [i] would yield (77, 829, 167)-net in base 3, but