Best Known (204, 239, s)-Nets in Base 2
(204, 239, 963)-Net over F2 — Constructive and digital
Digital (204, 239, 963)-net over F2, using
- net defined by OOA [i] based on linear OOA(2239, 963, F2, 35, 35) (dual of [(963, 35), 33466, 36]-NRT-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(2239, 16372, F2, 35) (dual of [16372, 16133, 36]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(2239, 16384, F2, 35) (dual of [16384, 16145, 36]-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(2239, 16372, F2, 35) (dual of [16372, 16133, 36]-code), using
(204, 239, 3092)-Net over F2 — Digital
Digital (204, 239, 3092)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2239, 3092, F2, 5, 35) (dual of [(3092, 5), 15221, 36]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2239, 3276, F2, 5, 35) (dual of [(3276, 5), 16141, 36]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2239, 16380, F2, 35) (dual of [16380, 16141, 36]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(2239, 16384, F2, 35) (dual of [16384, 16145, 36]-code), using
- OOA 5-folding [i] based on linear OA(2239, 16380, F2, 35) (dual of [16380, 16141, 36]-code), using
- discarding factors / shortening the dual code based on linear OOA(2239, 3276, F2, 5, 35) (dual of [(3276, 5), 16141, 36]-NRT-code), using
(204, 239, 117563)-Net in Base 2 — Upper bound on s
There is no (204, 239, 117564)-net in base 2, because
- 1 times m-reduction [i] would yield (204, 238, 117564)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 441738 429886 262866 925092 079025 840042 171158 311009 445657 823446 694169 520317 > 2238 [i]