Best Known (153, 153+18, s)-Nets in Base 2
(153, 153+18, 58254)-Net over F2 — Constructive and digital
Digital (153, 171, 58254)-net over F2, using
- net defined by OOA [i] based on linear OOA(2171, 58254, F2, 18, 18) (dual of [(58254, 18), 1048401, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(2171, 524286, F2, 18) (dual of [524286, 524115, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2171, 524287, F2, 18) (dual of [524287, 524116, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(2171, 524287, F2, 18) (dual of [524287, 524116, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(2171, 524286, F2, 18) (dual of [524286, 524115, 19]-code), using
(153, 153+18, 87381)-Net over F2 — Digital
Digital (153, 171, 87381)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2171, 87381, F2, 6, 18) (dual of [(87381, 6), 524115, 19]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2171, 524286, F2, 18) (dual of [524286, 524115, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2171, 524287, F2, 18) (dual of [524287, 524116, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(2171, 524287, F2, 18) (dual of [524287, 524116, 19]-code), using
- OOA 6-folding [i] based on linear OA(2171, 524286, F2, 18) (dual of [524286, 524115, 19]-code), using
(153, 153+18, 2174296)-Net in Base 2 — Upper bound on s
There is no (153, 171, 2174297)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 2993 161402 934852 181964 425254 780358 839342 200471 255278 > 2171 [i]