Best Known (177, s)-Sequences in Base 2
(177, 65)-Sequence over F2 — Constructive and digital
Digital (177, 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
(177, 80)-Sequence over F2 — Digital
Digital (177, 80)-sequence over F2, using
- t-expansion [i] based on digital (126, 80)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 126 and N(F) ≥ 81, using
(177, 186)-Sequence in Base 2 — Upper bound on s
There is no (177, 187)-sequence in base 2, because
- net from sequence [i] would yield (177, m, 188)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (177, 1682, 188)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(21682, 188, S2, 9, 1505), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 179745 896413 730294 307204 922027 608336 121100 945463 892178 688722 328101 949181 289906 101522 796910 624795 970783 099809 362138 721217 957139 556999 499218 533305 333295 476363 813171 721873 707617 195671 808044 613379 955943 848176 998216 342736 567100 833766 212669 971312 015192 584095 815797 391579 274488 680455 480200 718832 416653 101052 140655 936773 202348 897042 038033 881114 459249 827938 265566 783554 574874 046118 106673 281178 986855 112410 601203 049996 745916 490329 324781 767252 848533 872440 198726 064555 681700 339259 775886 121899 554931 537053 986130 568669 036544 / 753 > 21682 [i]
- extracting embedded OOA [i] would yield OOA(21682, 188, S2, 9, 1505), but
- m-reduction [i] would yield (177, 1682, 188)-net in base 2, but