Best Known (168−18, 168, s)-Nets in Base 2
(168−18, 168, 29130)-Net over F2 — Constructive and digital
Digital (150, 168, 29130)-net over F2, using
- net defined by OOA [i] based on linear OOA(2168, 29130, F2, 18, 18) (dual of [(29130, 18), 524172, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(2168, 262170, F2, 18) (dual of [262170, 262002, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2168, 262175, F2, 18) (dual of [262175, 262007, 19]-code), using
- 1 times truncation [i] based on linear OA(2169, 262176, F2, 19) (dual of [262176, 262007, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- linear OA(2163, 262144, F2, 19) (dual of [262144, 261981, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2127, 262144, F2, 15) (dual of [262144, 262017, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- 1 times truncation [i] based on linear OA(2169, 262176, F2, 19) (dual of [262176, 262007, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2168, 262175, F2, 18) (dual of [262175, 262007, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(2168, 262170, F2, 18) (dual of [262170, 262002, 19]-code), using
(168−18, 168, 52435)-Net over F2 — Digital
Digital (150, 168, 52435)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2168, 52435, F2, 5, 18) (dual of [(52435, 5), 262007, 19]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2168, 262175, F2, 18) (dual of [262175, 262007, 19]-code), using
- 1 times truncation [i] based on linear OA(2169, 262176, F2, 19) (dual of [262176, 262007, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- linear OA(2163, 262144, F2, 19) (dual of [262144, 261981, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2127, 262144, F2, 15) (dual of [262144, 262017, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- 1 times truncation [i] based on linear OA(2169, 262176, F2, 19) (dual of [262176, 262007, 20]-code), using
- OOA 5-folding [i] based on linear OA(2168, 262175, F2, 18) (dual of [262175, 262007, 19]-code), using
(168−18, 168, 1725737)-Net in Base 2 — Upper bound on s
There is no (150, 168, 1725738)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 374 145193 574319 550466 034315 851877 858332 851409 355431 > 2168 [i]