Best Known (33, 67, s)-Nets in Base 128
(33, 67, 963)-Net over F128 — Constructive and digital
Digital (33, 67, 963)-net over F128, using
- net defined by OOA [i] based on linear OOA(12867, 963, F128, 34, 34) (dual of [(963, 34), 32675, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(12867, 16371, F128, 34) (dual of [16371, 16304, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(12867, 16384, F128, 34) (dual of [16384, 16317, 35]-code), using
- an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- discarding factors / shortening the dual code based on linear OA(12867, 16384, F128, 34) (dual of [16384, 16317, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(12867, 16371, F128, 34) (dual of [16371, 16304, 35]-code), using
(33, 67, 3462)-Net over F128 — Digital
Digital (33, 67, 3462)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12867, 3462, F128, 4, 34) (dual of [(3462, 4), 13781, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12867, 4096, F128, 4, 34) (dual of [(4096, 4), 16317, 35]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12867, 16384, F128, 34) (dual of [16384, 16317, 35]-code), using
- an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- OOA 4-folding [i] based on linear OA(12867, 16384, F128, 34) (dual of [16384, 16317, 35]-code), using
- discarding factors / shortening the dual code based on linear OOA(12867, 4096, F128, 4, 34) (dual of [(4096, 4), 16317, 35]-NRT-code), using
(33, 67, large)-Net in Base 128 — Upper bound on s
There is no (33, 67, large)-net in base 128, because
- 32 times m-reduction [i] would yield (33, 35, large)-net in base 128, but