Best Known (151, s)-Sequences in Base 4
(151, 129)-Sequence over F4 — Constructive and digital
Digital (151, 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
(151, 214)-Sequence over F4 — Digital
Digital (151, 214)-sequence over F4, using
- t-expansion [i] based on 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
(151, 469)-Sequence in Base 4 — Upper bound on s
There is no (151, 470)-sequence in base 4, because
- net from sequence [i] would yield (151, m, 471)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (151, 2349, 471)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42349, 471, S4, 5, 2198), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 20 039065 437755 736471 973514 985034 251849 050573 255670 966499 656812 617522 485653 534808 801176 856476 109291 910905 981122 256447 520904 352345 345961 503595 688687 805863 491979 292424 382854 542184 916240 237479 024666 033846 426026 616496 238357 512809 564991 449610 826050 131571 706151 073887 538985 734805 362931 509253 992557 573319 644964 958404 152708 746368 206615 295207 196607 310084 488021 683896 495943 381573 998135 746241 703750 596640 074563 564022 367536 881959 467806 706390 031971 933846 401130 377620 416415 547474 793659 188727 787488 767267 762872 735256 776041 378098 367147 329307 506710 175522 773472 367445 385584 850168 698967 794276 727425 703178 168459 343931 209448 355969 325449 738927 798044 928434 025805 737683 162262 791980 643762 150586 027257 231422 390444 149303 590748 103681 616843 123417 676683 412722 124121 278677 674511 196447 786101 166924 471496 902814 587758 250729 935140 409697 533450 415001 470178 009909 081430 205248 364028 004704 480850 757686 488557 272079 584117 052188 799564 445492 036351 190249 005214 984906 371081 949978 823361 152744 244222 778161 886499 979855 792455 710122 254885 716202 731553 658234 948986 242531 907489 113496 767415 196329 583301 751737 297266 921166 010809 852316 449024 747084 291968 686701 611658 934071 969977 629987 894112 508911 465162 062099 638409 357996 797815 834562 739678 292274 082542 822819 029227 880397 028099 751772 902842 699730 874448 297781 318695 651149 350084 765009 202673 798551 944539 919327 060374 249609 487837 984080 611669 823646 676302 318557 351994 580463 703032 025302 388578 908997 156333 400595 569172 915639 547428 611150 577664 / 733 > 42349 [i]
- extracting embedded OOA [i] would yield OOA(42349, 471, S4, 5, 2198), but
- m-reduction [i] would yield (151, 2349, 471)-net in base 4, but