Best Known (36, 73, s)-Nets in Base 128
(36, 73, 910)-Net over F128 — Constructive and digital
Digital (36, 73, 910)-net over F128, using
- net defined by OOA [i] based on linear OOA(12873, 910, F128, 37, 37) (dual of [(910, 37), 33597, 38]-NRT-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(12873, 16381, F128, 37) (dual of [16381, 16308, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(12873, 16384, F128, 37) (dual of [16384, 16311, 38]-code), using
- an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- discarding factors / shortening the dual code based on linear OA(12873, 16384, F128, 37) (dual of [16384, 16311, 38]-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(12873, 16381, F128, 37) (dual of [16381, 16308, 38]-code), using
(36, 73, 3506)-Net over F128 — Digital
Digital (36, 73, 3506)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12873, 3506, F128, 4, 37) (dual of [(3506, 4), 13951, 38]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12873, 4096, F128, 4, 37) (dual of [(4096, 4), 16311, 38]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12873, 16384, F128, 37) (dual of [16384, 16311, 38]-code), using
- an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- OOA 4-folding [i] based on linear OA(12873, 16384, F128, 37) (dual of [16384, 16311, 38]-code), using
- discarding factors / shortening the dual code based on linear OOA(12873, 4096, F128, 4, 37) (dual of [(4096, 4), 16311, 38]-NRT-code), using
(36, 73, large)-Net in Base 128 — Upper bound on s
There is no (36, 73, large)-net in base 128, because
- 35 times m-reduction [i] would yield (36, 38, large)-net in base 128, but