Best Known (134, s)-Sequences in Base 3
(134, 77)-Sequence over F3 — Constructive and digital
Digital (134, 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
(134, 119)-Sequence over F3 — Digital
Digital (134, 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
(134, 280)-Sequence in Base 3 — Upper bound on s
There is no (134, 281)-sequence in base 3, because
- net from sequence [i] would yield (134, m, 282)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (134, 1685, 282)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31685, 282, S3, 6, 1551), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 392 421498 736069 208912 881196 149404 625817 043526 798235 658281 179948 053670 586318 656959 126107 237141 588977 325304 335227 050935 566270 140333 111961 369336 270068 392261 214019 606681 791296 468335 547425 395124 502173 000369 648628 777734 274086 614431 797966 251992 736475 095358 822192 028643 854949 510951 971097 099957 997669 719678 781691 834747 104799 967510 983041 748697 385908 266259 486147 809931 061992 923394 136683 789170 121596 172192 273791 270036 298386 018438 414470 013949 627991 343054 100223 933779 084845 166539 897595 795489 970669 146832 308682 547499 499950 079717 682717 721113 472748 125616 971634 771372 961761 304324 160238 501619 921442 337841 539095 327732 615539 307599 056443 208275 952286 440713 744357 692719 605055 409981 126380 771895 043415 070589 189302 763967 799859 911838 710905 644180 558822 812518 270270 801627 237892 138384 458806 951539 490970 127723 643504 438183 467724 823939 791963 / 388 > 31685 [i]
- extracting embedded OOA [i] would yield OOA(31685, 282, S3, 6, 1551), but
- m-reduction [i] would yield (134, 1685, 282)-net in base 3, but