Best Known (36, 48, s)-Nets in Base 2
(36, 48, 75)-Net over F2 — Constructive and digital
Digital (36, 48, 75)-net over F2, using
- trace code for nets [i] based on digital (4, 16, 25)-net over F8, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 4 and N(F) ≥ 25, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
(36, 48, 128)-Net over F2 — Digital
Digital (36, 48, 128)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(248, 128, F2, 2, 12) (dual of [(128, 2), 208, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(248, 256, F2, 12) (dual of [256, 208, 13]-code), using
- 1 times truncation [i] based on linear OA(249, 257, F2, 13) (dual of [257, 208, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 257 | 216−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(249, 257, F2, 13) (dual of [257, 208, 14]-code), using
- OOA 2-folding [i] based on linear OA(248, 256, F2, 12) (dual of [256, 208, 13]-code), using
(36, 48, 757)-Net in Base 2 — Upper bound on s
There is no (36, 48, 758)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 281 579876 093632 > 248 [i]