Best Known (242, s)-Sequences in Base 4
(242, 257)-Sequence over F4 — Constructive and digital
Digital (242, 257)-sequence over F4, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 225 and N(F) ≥ 258, using
- T8 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) = 225 and N(F) ≥ 258, using
(242, 300)-Sequence over F4 — Digital
Digital (242, 300)-sequence over F4, using
- t-expansion [i] based on digital (234, 300)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 234 and N(F) ≥ 301, using
(242, 743)-Sequence in Base 4 — Upper bound on s
There is no (242, 744)-sequence in base 4, because
- net from sequence [i] would yield (242, m, 745)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (242, 3719, 745)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43719, 745, S4, 5, 3477), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 25715 259867 308215 718063 764457 550401 596790 374102 504115 442786 121650 018469 035032 146766 449954 770527 424357 771972 321143 564763 699982 869609 211466 883967 322649 165023 057932 956734 806443 144980 854365 145190 381489 163271 162401 376427 558218 818523 331553 819230 164518 279994 909793 538614 057908 479899 651794 421708 205422 265029 922616 186320 918046 510311 053132 534674 322729 258316 841869 786296 297235 955826 038180 055821 350069 765463 770304 773759 893872 147543 153481 544502 749294 246571 825797 963781 955232 107921 742275 140582 261612 685340 560974 765797 250913 539061 076388 244135 069026 079999 747107 161860 883296 215446 152761 823905 886809 932680 426042 767463 891274 557689 448223 819723 967676 239659 978946 207464 059129 069932 176542 574515 509999 079380 579788 870701 597837 935720 745074 562269 613257 520663 335140 341363 953583 056529 321392 922770 274376 036774 002013 301224 728558 417939 766379 162078 612584 907713 721767 690238 467972 136881 118131 005870 073464 891112 373789 058151 640795 909495 506052 480315 581909 048867 296678 773083 365922 575783 560072 416096 711061 053560 287842 408282 142311 632787 005578 539324 895878 196452 103861 857578 203954 571067 584042 120591 088315 806758 852768 193147 912660 747889 266895 028732 981922 665419 639764 699654 850855 015197 329407 432622 184755 871815 296104 370657 150577 348148 185889 969520 873629 468775 943384 348386 153503 918599 127244 221671 422891 063488 622282 321385 976000 187073 557488 247262 391784 175733 185321 748636 712544 652947 347799 777569 272558 275441 340694 984556 793410 321859 853510 365962 617220 875927 025787 592204 463202 179351 835042 279950 949995 371365 304188 223036 233485 628400 688976 236749 459714 178531 422084 391137 177429 904071 516089 488689 993006 226799 351232 445373 574068 516300 613913 569561 525226 835127 713716 678169 184953 287418 871695 069933 707278 548542 025149 570490 654652 755059 893302 095910 654758 119629 820192 818799 082788 174995 943002 501019 604141 783781 118975 971212 933659 213677 435267 041559 450716 358694 227607 090294 619032 926932 042531 433863 319510 074544 183855 014558 621883 235768 423839 080315 497829 342674 055553 801120 297885 306731 574219 167105 266376 830914 388230 741393 244713 667688 974719 096957 726688 528305 070965 394226 014416 265961 594216 747061 006386 679633 155742 746741 926238 621024 359376 946562 602622 053515 797510 134844 960322 997018 128607 728503 585510 221288 571574 435721 596419 585542 124236 368824 594803 389521 895305 517395 458415 412898 646831 675846 748843 517535 540544 353228 306457 296896 / 1739 > 43719 [i]
- extracting embedded OOA [i] would yield OOA(43719, 745, S4, 5, 3477), but
- m-reduction [i] would yield (242, 3719, 745)-net in base 4, but