Best Known (200, s)-Sequences in Base 2
(200, 65)-Sequence over F2 — Constructive and digital
Digital (200, 65)-sequence over F2, using
- t-expansion [i] based on digital (163, 65)-sequence over F2, using
- base reduction for sequences [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 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) = 49 and N(F) ≥ 66, using
- base reduction for sequences [i] based on digital (49, 65)-sequence over F4, using
(200, 90)-Sequence over F2 — Digital
Digital (200, 90)-sequence over F2, using
- t-expansion [i] based on digital (190, 90)-sequence over F2, using
- base reduction for sequences [i] based on digital (50, 90)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 50 and N(F) ≥ 91, using
- base reduction for sequences [i] based on digital (50, 90)-sequence over F4, using
(200, 210)-Sequence in Base 2 — Upper bound on s
There is no (200, 211)-sequence in base 2, because
- net from sequence [i] would yield (200, m, 212)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (200, 1474, 212)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(21474, 212, S2, 7, 1274), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 719 170794 843990 166734 688893 457449 385510 221806 933510 608403 806359 799390 528475 867679 003360 022603 585089 803259 595628 835589 050373 871614 686588 415827 443444 001294 201116 212906 298232 642351 595171 259922 459936 655680 621445 637257 770674 088188 501705 451724 831457 397130 832956 914770 751962 865303 857066 406538 629165 991556 682571 885824 218291 930812 568475 222926 864244 647425 956374 048238 875019 564476 858523 229962 951909 707901 920288 089526 793617 129102 639517 712188 066848 525237 878784 / 1275 > 21474 [i]
- extracting embedded OOA [i] would yield OOA(21474, 212, S2, 7, 1274), but
- m-reduction [i] would yield (200, 1474, 212)-net in base 2, but