Best Known (238−34, 238, s)-Nets in Base 2
(238−34, 238, 963)-Net over F2 — Constructive and digital
Digital (204, 238, 963)-net over F2, using
- net defined by OOA [i] based on linear OOA(2238, 963, F2, 34, 34) (dual of [(963, 34), 32504, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(2238, 16371, F2, 34) (dual of [16371, 16133, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(2238, 16383, F2, 34) (dual of [16383, 16145, 35]-code), using
- 1 times truncation [i] based on linear OA(2239, 16384, F2, 35) (dual of [16384, 16145, 36]-code), using
- an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- 1 times truncation [i] based on linear OA(2239, 16384, F2, 35) (dual of [16384, 16145, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(2238, 16383, F2, 34) (dual of [16383, 16145, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(2238, 16371, F2, 34) (dual of [16371, 16133, 35]-code), using
(238−34, 238, 3276)-Net over F2 — Digital
Digital (204, 238, 3276)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2238, 3276, F2, 5, 34) (dual of [(3276, 5), 16142, 35]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2238, 16380, F2, 34) (dual of [16380, 16142, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(2238, 16383, F2, 34) (dual of [16383, 16145, 35]-code), using
- 1 times truncation [i] based on linear OA(2239, 16384, F2, 35) (dual of [16384, 16145, 36]-code), using
- an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- 1 times truncation [i] based on linear OA(2239, 16384, F2, 35) (dual of [16384, 16145, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(2238, 16383, F2, 34) (dual of [16383, 16145, 35]-code), using
- OOA 5-folding [i] based on linear OA(2238, 16380, F2, 34) (dual of [16380, 16142, 35]-code), using
(238−34, 238, 117563)-Net in Base 2 — Upper bound on s
There is no (204, 238, 117564)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 441738 429886 262866 925092 079025 840042 171158 311009 445657 823446 694169 520317 > 2238 [i]