Best Known (69−30, 69, s)-Nets in Base 2
(69−30, 69, 33)-Net over F2 — Constructive and digital
Digital (39, 69, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 39 and N(F) ≥ 33, using
(69−30, 69, 34)-Net over F2 — Digital
Digital (39, 69, 34)-net over F2, using
(69−30, 69, 135)-Net in Base 2 — Upper bound on s
There is no (39, 69, 136)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 644 893210 740430 847408 > 269 [i]
- extracting embedded orthogonal array [i] would yield OA(269, 136, S2, 30), but
- the linear programming bound shows that M ≥ 9953 606881 455955 393180 647209 954684 775902 917778 898747 969803 296803 127296 / 16 615467 389796 179841 085069 094075 585803 909505 010295 > 269 [i]