Best Known (148, s)-Sequences in Base 4
(148, 129)-Sequence over F4 — Constructive and digital
Digital (148, 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
(148, 214)-Sequence over F4 — Digital
Digital (148, 214)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 148 and N(F) ≥ 215, using
(148, 460)-Sequence in Base 4 — Upper bound on s
There is no (148, 461)-sequence in base 4, because
- net from sequence [i] would yield (148, m, 462)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (148, 2304, 462)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42304, 462, S4, 5, 2156), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 16243 440010 339968 008084 154325 114848 672524 656151 137009 190515 714333 272982 696379 194057 747007 542242 623604 207900 645323 014000 343215 982556 154728 889278 949333 338531 122351 947355 111395 387145 693620 927369 770427 597065 420406 706663 188239 837643 975671 865604 370394 609955 497688 209583 982613 250124 384823 543460 370012 388060 988169 475310 834926 036326 373936 436361 107611 831713 110957 564785 561321 777575 090280 277537 044256 013685 485292 430582 337782 813302 453486 977657 836747 117596 396986 741050 371137 500172 035258 757225 944845 319167 706443 184500 680078 383864 530099 877118 128052 473090 813854 884096 751175 503215 074883 168164 525600 605133 133644 377749 847736 447658 061266 518008 563281 777500 420217 605403 689249 179119 819907 417517 944277 712532 806170 790258 766116 604692 294286 269876 115240 347996 639978 528315 499232 933838 985458 377291 453694 102246 595832 881381 292264 038297 231767 420952 552821 383934 942847 945534 289530 403632 124195 348144 373792 950022 854145 598203 000355 729728 343351 537845 027516 928968 471981 016278 926104 111688 183890 403518 172640 652782 969967 875886 351311 668686 722733 645025 431596 590477 144174 096911 908406 774699 831050 338131 626105 411789 674630 521921 059426 218783 352756 054037 078021 857506 661928 623893 388816 743626 841635 554022 528258 736105 987850 493322 515584 089137 780707 283134 701389 750818 476962 065625 757800 257434 080141 504920 278750 912029 201000 542094 373982 252884 334262 580719 119752 548606 491233 795227 066462 532153 960522 755962 477774 317157 050368 910880 960091 202438 535535 656960 / 719 > 42304 [i]
- extracting embedded OOA [i] would yield OOA(42304, 462, S4, 5, 2156), but
- m-reduction [i] would yield (148, 2304, 462)-net in base 4, but