Best Known (247−26, 247, s)-Nets in Base 2
(247−26, 247, 40329)-Net over F2 — Constructive and digital
Digital (221, 247, 40329)-net over F2, using
- net defined by OOA [i] based on linear OOA(2247, 40329, F2, 26, 26) (dual of [(40329, 26), 1048307, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(2247, 524277, F2, 26) (dual of [524277, 524030, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2247, 524287, F2, 26) (dual of [524287, 524040, 27]-code), using
- 1 times truncation [i] based on linear OA(2248, 524288, F2, 27) (dual of [524288, 524040, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- 1 times truncation [i] based on linear OA(2248, 524288, F2, 27) (dual of [524288, 524040, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2247, 524287, F2, 26) (dual of [524287, 524040, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(2247, 524277, F2, 26) (dual of [524277, 524030, 27]-code), using
(247−26, 247, 74898)-Net over F2 — Digital
Digital (221, 247, 74898)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2247, 74898, F2, 7, 26) (dual of [(74898, 7), 524039, 27]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2247, 524286, F2, 26) (dual of [524286, 524039, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2247, 524287, F2, 26) (dual of [524287, 524040, 27]-code), using
- 1 times truncation [i] based on linear OA(2248, 524288, F2, 27) (dual of [524288, 524040, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- 1 times truncation [i] based on linear OA(2248, 524288, F2, 27) (dual of [524288, 524040, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2247, 524287, F2, 26) (dual of [524287, 524040, 27]-code), using
- OOA 7-folding [i] based on linear OA(2247, 524286, F2, 26) (dual of [524286, 524039, 27]-code), using
(247−26, 247, 2971483)-Net in Base 2 — Upper bound on s
There is no (221, 247, 2971484)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 226 156947 225384 078191 617909 481242 581731 732374 495302 924175 193242 206718 149564 > 2247 [i]