Best Known (99, s)-Sequences in Base 7
(99, 79)-Sequence over F7 — Constructive and digital
Digital (99, 79)-sequence over F7, using
- Niederreiter–Xing sequence construction III based on function field F2/F7 with g(F2) = 21, N(F2) ≥ 2, and N(F2) + N2(F2) ≥ 80 from GarcÃa–Stichtenoth tower as constant field extension [i]
(99, 104)-Sequence over F7 — Digital
Digital (99, 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
(99, 617)-Sequence in Base 7 — Upper bound on s
There is no (99, 618)-sequence in base 7, because
- net from sequence [i] would yield (99, m, 619)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (99, 1853, 619)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(71853, 619, S7, 3, 1754), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 71 311385 041444 333024 873739 669581 949509 212793 172548 277173 670132 226861 738440 157924 235652 694714 579852 419071 568350 158755 918877 825717 942351 978637 706414 004834 438211 777615 428537 412312 802969 390964 922668 446961 118783 359989 904470 432180 264091 667291 581316 218116 576737 852570 618215 465715 329011 078602 640729 768363 350454 292201 902756 309046 700767 265280 353661 211269 911168 272489 988023 375237 654873 502211 710416 716659 407841 654850 037318 826811 270191 948965 234270 302472 543646 215895 548758 777487 904510 817100 703236 063866 505948 000481 500912 041175 061181 207828 809464 936560 580196 459899 352485 431990 732838 232793 122732 271837 440669 381697 238946 982209 299895 588004 400726 867732 158464 282490 589433 500731 696764 644678 911900 988760 101833 779576 441279 181180 992450 385752 001898 349338 629085 935125 932324 586966 076792 598107 385739 888578 595981 284269 423763 141656 771925 310960 553211 273697 415244 176414 654358 606585 307861 405936 026476 504352 392867 295016 189822 962583 605877 492927 506318 071312 239002 318086 939173 319691 243242 785446 688643 397967 221200 068676 113253 069405 824861 133979 490115 472491 220025 549851 043184 160453 050493 261893 160513 151972 205331 692698 196969 504925 108013 443131 185720 050158 879115 332424 463019 720200 272671 196426 439011 472572 403995 657969 036817 971394 731116 914757 476870 209735 006866 726494 088761 016008 789242 413583 824786 394839 574594 255842 044030 588002 695666 926679 425601 803701 781468 325547 736932 047147 577163 256196 709527 365797 311735 908357 798038 421769 295841 722463 982983 663728 505472 689869 884595 376328 214633 782786 958669 258185 508898 021559 724265 082043 970290 881452 699524 332858 822343 826040 180137 176644 142185 437054 059387 692163 493493 137964 503256 857339 / 65 > 71853 [i]
- extracting embedded OOA [i] would yield OOA(71853, 619, S7, 3, 1754), but
- m-reduction [i] would yield (99, 1853, 619)-net in base 7, but