Best Known (34, 69, s)-Nets in Base 128
(34, 69, 963)-Net over F128 — Constructive and digital
Digital (34, 69, 963)-net over F128, using
- net defined by OOA [i] based on linear OOA(12869, 963, F128, 35, 35) (dual of [(963, 35), 33636, 36]-NRT-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(12869, 16372, F128, 35) (dual of [16372, 16303, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(12869, 16384, F128, 35) (dual of [16384, 16315, 36]-code), using
- an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- discarding factors / shortening the dual code based on linear OA(12869, 16384, F128, 35) (dual of [16384, 16315, 36]-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(12869, 16372, F128, 35) (dual of [16372, 16303, 36]-code), using
(34, 69, 3474)-Net over F128 — Digital
Digital (34, 69, 3474)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12869, 3474, F128, 4, 35) (dual of [(3474, 4), 13827, 36]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12869, 4096, F128, 4, 35) (dual of [(4096, 4), 16315, 36]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12869, 16384, F128, 35) (dual of [16384, 16315, 36]-code), using
- an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- OOA 4-folding [i] based on linear OA(12869, 16384, F128, 35) (dual of [16384, 16315, 36]-code), using
- discarding factors / shortening the dual code based on linear OOA(12869, 4096, F128, 4, 35) (dual of [(4096, 4), 16315, 36]-NRT-code), using
(34, 69, large)-Net in Base 128 — Upper bound on s
There is no (34, 69, large)-net in base 128, because
- 33 times m-reduction [i] would yield (34, 36, large)-net in base 128, but