Best Known (115, s)-Sequences in Base 2
(115, 56)-Sequence over F2 — Constructive and digital
Digital (115, 56)-sequence over F2, using
- t-expansion [i] based on digital (110, 56)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 8 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
(115, 72)-Sequence over F2 — Digital
Digital (115, 72)-sequence over F2, using
- t-expansion [i] based on digital (114, 72)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 114 and N(F) ≥ 73, using
(115, 124)-Sequence in Base 2 — Upper bound on s
There is no (115, 125)-sequence in base 2, because
- net from sequence [i] would yield (115, m, 126)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (115, 872, 126)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2872, 126, S2, 7, 757), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 16 374180 089863 892084 551852 235590 734207 022226 425336 789578 589175 265662 099679 082448 895376 740280 484064 680649 679028 778893 167556 453986 820065 765343 325154 113812 958001 635138 730971 970782 741331 409915 789922 927177 018658 507941 374598 426355 767971 527336 024484 566388 593587 879065 681920 / 379 > 2872 [i]
- extracting embedded OOA [i] would yield OOA(2872, 126, S2, 7, 757), but
- m-reduction [i] would yield (115, 872, 126)-net in base 2, but