Best Known (150, 150+31, s)-Nets in Base 2
(150, 150+31, 380)-Net over F2 — Constructive and digital
Digital (150, 181, 380)-net over F2, using
- 21 times duplication [i] based on digital (149, 180, 380)-net over F2, using
- trace code for nets [i] based on digital (5, 36, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- trace code for nets [i] based on digital (5, 36, 76)-net over F32, using
(150, 150+31, 1024)-Net over F2 — Digital
Digital (150, 181, 1024)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2181, 1024, F2, 4, 31) (dual of [(1024, 4), 3915, 32]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2181, 4096, F2, 31) (dual of [4096, 3915, 32]-code), using
- an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- OOA 4-folding [i] based on linear OA(2181, 4096, F2, 31) (dual of [4096, 3915, 32]-code), using
(150, 150+31, 26288)-Net in Base 2 — Upper bound on s
There is no (150, 181, 26289)-net in base 2, because
- 1 times m-reduction [i] would yield (150, 180, 26289)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1 533058 208277 459894 978640 042697 257450 569867 035049 566208 > 2180 [i]