Best Known (126−34, 126, s)-Nets in Base 16
(126−34, 126, 3855)-Net over F16 — Constructive and digital
Digital (92, 126, 3855)-net over F16, using
- 161 times duplication [i] based on digital (91, 125, 3855)-net over F16, using
- net defined by OOA [i] based on linear OOA(16125, 3855, F16, 34, 34) (dual of [(3855, 34), 130945, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(16125, 65535, F16, 34) (dual of [65535, 65410, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(16125, 65536, F16, 34) (dual of [65536, 65411, 35]-code), using
- an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- discarding factors / shortening the dual code based on linear OA(16125, 65536, F16, 34) (dual of [65536, 65411, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(16125, 65535, F16, 34) (dual of [65535, 65410, 35]-code), using
- net defined by OOA [i] based on linear OOA(16125, 3855, F16, 34, 34) (dual of [(3855, 34), 130945, 35]-NRT-code), using
(126−34, 126, 43074)-Net over F16 — Digital
Digital (92, 126, 43074)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16126, 43074, F16, 34) (dual of [43074, 42948, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(16126, 65541, F16, 34) (dual of [65541, 65415, 35]-code), using
- 1 times code embedding in larger space [i] based on linear OA(16125, 65540, F16, 34) (dual of [65540, 65415, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(32) [i] based on
- linear OA(16125, 65536, F16, 34) (dual of [65536, 65411, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(16121, 65536, F16, 33) (dual of [65536, 65415, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(160, 4, F16, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(33) ⊂ Ce(32) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(16125, 65540, F16, 34) (dual of [65540, 65415, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(16126, 65541, F16, 34) (dual of [65541, 65415, 35]-code), using
(126−34, 126, large)-Net in Base 16 — Upper bound on s
There is no (92, 126, large)-net in base 16, because
- 32 times m-reduction [i] would yield (92, 94, large)-net in base 16, but