Best Known (62, s)-Sequences in Base 7
(62, 53)-Sequence over F7 — Constructive and digital
Digital (62, 53)-sequence over F7, using
- t-expansion [i] based on digital (61, 53)-sequence over F7, using
- base reduction for sequences [i] based on digital (4, 53)-sequence over F49, using
(62, 104)-Sequence over F7 — Digital
Digital (62, 104)-sequence over F7, using
- t-expansion [i] based on digital (43, 104)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 43 and N(F) ≥ 105, using
(62, 392)-Sequence in Base 7 — Upper bound on s
There is no (62, 393)-sequence in base 7, because
- net from sequence [i] would yield (62, m, 394)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (62, 1178, 394)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(71178, 394, S7, 3, 1116), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 382 628029 516626 355572 657127 236652 787520 703967 355650 944019 396160 377626 435425 643486 054921 144121 694910 285184 854476 662810 954321 595439 463874 401268 813655 538107 002713 650229 679072 518534 884954 478313 855560 414923 127150 691265 972953 361307 983469 002185 963757 780159 528577 106492 403815 969117 622128 297621 940856 475925 915592 545602 295891 510564 269605 284736 727704 786461 153633 277355 680419 227615 353243 588188 317214 967688 440630 642727 890308 253924 515967 710781 286874 173997 484757 702297 360818 337611 576120 674221 871825 845025 902687 110353 324783 340330 089618 408976 797259 536821 223034 644346 965476 629805 956205 244674 505254 573650 146398 121088 461555 862036 641643 254176 401818 074922 579026 809128 815439 963913 837880 924159 626487 693258 825618 561760 285355 107095 325972 108232 774700 737363 363732 583970 937582 451075 788461 715863 048379 377950 364076 653155 630225 244420 065752 699279 354441 517772 122735 905593 397063 095400 251514 089880 664755 912498 810466 713257 789527 054131 653149 028856 936508 463280 889207 441608 052634 868447 083356 837803 045571 245488 683563 477541 642966 223418 086309 / 1117 > 71178 [i]
- extracting embedded OOA [i] would yield OOA(71178, 394, S7, 3, 1116), but
- m-reduction [i] would yield (62, 1178, 394)-net in base 7, but