Best Known (127, s)-Sequences in Base 3
(127, 77)-Sequence over F3 — Constructive and digital
Digital (127, 77)-sequence over F3, using
- t-expansion [i] based on digital (121, 77)-sequence over F3, using
- base reduction for sequences [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- base reduction for sequences [i] based on digital (22, 77)-sequence over F9, using
(127, 119)-Sequence over F3 — Digital
Digital (127, 119)-sequence over F3, using
- t-expansion [i] based on digital (113, 119)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 113 and N(F) ≥ 120, using
(127, 266)-Sequence in Base 3 — Upper bound on s
There is no (127, 267)-sequence in base 3, because
- net from sequence [i] would yield (127, m, 268)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (127, 1601, 268)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31601, 268, S3, 6, 1474), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 26533 651597 164716 195958 558427 221436 255554 542613 541837 575285 916732 850043 018730 986557 236832 945776 801103 044660 797479 146109 384851 629106 496645 046633 856346 854856 830820 786960 149206 416332 851636 398078 981151 294770 281316 031093 727337 344291 475707 702266 420818 766355 871424 052020 953339 735338 996304 236158 411727 791167 606953 563507 012134 649288 470050 220801 491819 550681 557551 459435 831479 917627 381893 367454 730406 462916 373984 322624 574299 591680 895191 340147 204358 836219 056067 587485 383285 084886 836499 316963 728718 250960 870694 146979 524577 978421 690500 604938 099550 375885 425664 259609 141472 027282 755627 323496 869703 253691 371038 595893 911996 974962 695629 934808 113827 675053 174856 773873 113265 389508 932639 923011 186641 431554 516936 164751 530230 750382 637442 550904 207082 380849 586207 469786 923971 772959 598176 993071 / 295 > 31601 [i]
- extracting embedded OOA [i] would yield OOA(31601, 268, S3, 6, 1474), but
- m-reduction [i] would yield (127, 1601, 268)-net in base 3, but