Best Known (240−26, 240, s)-Nets in Base 2
(240−26, 240, 20167)-Net over F2 — Constructive and digital
Digital (214, 240, 20167)-net over F2, using
- net defined by OOA [i] based on linear OOA(2240, 20167, F2, 26, 26) (dual of [(20167, 26), 524102, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(2240, 262171, F2, 26) (dual of [262171, 261931, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2240, 262175, F2, 26) (dual of [262175, 261935, 27]-code), using
- 1 times truncation [i] based on linear OA(2241, 262176, F2, 27) (dual of [262176, 261935, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(2235, 262144, F2, 27) (dual of [262144, 261909, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2199, 262144, F2, 23) (dual of [262144, 261945, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(26) ⊂ Ce(22) [i] based on
- 1 times truncation [i] based on linear OA(2241, 262176, F2, 27) (dual of [262176, 261935, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2240, 262175, F2, 26) (dual of [262175, 261935, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(2240, 262171, F2, 26) (dual of [262171, 261931, 27]-code), using
(240−26, 240, 40396)-Net over F2 — Digital
Digital (214, 240, 40396)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2240, 40396, F2, 6, 26) (dual of [(40396, 6), 242136, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2240, 43695, F2, 6, 26) (dual of [(43695, 6), 261930, 27]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2240, 262170, F2, 26) (dual of [262170, 261930, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2240, 262175, F2, 26) (dual of [262175, 261935, 27]-code), using
- 1 times truncation [i] based on linear OA(2241, 262176, F2, 27) (dual of [262176, 261935, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(2235, 262144, F2, 27) (dual of [262144, 261909, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2199, 262144, F2, 23) (dual of [262144, 261945, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(26) ⊂ Ce(22) [i] based on
- 1 times truncation [i] based on linear OA(2241, 262176, F2, 27) (dual of [262176, 261935, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2240, 262175, F2, 26) (dual of [262175, 261935, 27]-code), using
- OOA 6-folding [i] based on linear OA(2240, 262170, F2, 26) (dual of [262170, 261930, 27]-code), using
- discarding factors / shortening the dual code based on linear OOA(2240, 43695, F2, 6, 26) (dual of [(43695, 6), 261930, 27]-NRT-code), using
(240−26, 240, 2045874)-Net in Base 2 — Upper bound on s
There is no (214, 240, 2045875)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 766852 748147 822965 353228 587766 114885 958155 410405 345511 544316 953959 397376 > 2240 [i]