Best Known (136, s)-Sequences in Base 4
(136, 129)-Sequence over F4 — Constructive and digital
Digital (136, 129)-sequence over F4, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
(136, 175)-Sequence over F4 — Digital
Digital (136, 175)-sequence over F4, using
- t-expansion [i] based on digital (125, 175)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 125 and N(F) ≥ 176, using
(136, 423)-Sequence in Base 4 — Upper bound on s
There is no (136, 424)-sequence in base 4, because
- net from sequence [i] would yield (136, m, 425)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (136, 2119, 425)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42119, 425, S4, 5, 1983), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 196878 778592 532232 150726 721280 127111 349338 787383 494636 479483 334591 635089 997806 041822 710256 502177 354873 978026 030785 243914 866147 602791 337044 500825 571718 897502 833867 768092 395865 758231 430615 107261 896784 300208 407962 053111 704255 152671 342070 379938 038496 673505 113432 045858 616182 013214 040158 639307 261387 594697 290888 246531 097179 700035 263060 184024 953800 747077 007027 949381 177367 686282 015291 024083 077779 993790 248551 032856 779177 742511 296857 131488 186276 895008 133975 014669 321769 342057 968581 815943 706943 857331 985476 458390 476381 869247 119500 639194 406280 074272 238731 556326 404552 491817 546573 354587 287483 906898 045904 450387 706122 860697 571820 376535 661486 576221 247588 264459 528952 598900 829480 291003 524131 083498 743257 957059 904178 627672 376787 623472 814459 942893 092894 490484 130988 885602 104164 775165 222294 198308 130814 668044 813935 572861 760393 972650 285728 567041 905462 517284 919315 618966 586284 382470 172277 287589 059795 158883 892714 016329 931935 071345 899775 102001 837389 801251 163641 930066 105644 038663 923508 966673 569219 423678 718104 866135 446060 599209 621740 621885 394753 405599 598376 469307 431785 298315 257706 646796 735684 214018 340148 785872 306495 315185 117829 855026 047984 641494 490391 655406 981122 747072 880066 731437 806687 534028 332817 707794 165277 917481 958024 956260 135305 496062 965149 613633 900219 229598 806786 272911 003942 043510 636544 / 31 > 42119 [i]
- extracting embedded OOA [i] would yield OOA(42119, 425, S4, 5, 1983), but
- m-reduction [i] would yield (136, 2119, 425)-net in base 4, but