Best Known (14, 14+8, s)-Nets in Base 16
(14, 14+8, 1024)-Net over F16 — Constructive and digital
Digital (14, 22, 1024)-net over F16, using
- net defined by OOA [i] based on linear OOA(1622, 1024, F16, 8, 8) (dual of [(1024, 8), 8170, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(1622, 4096, F16, 8) (dual of [4096, 4074, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OA 4-folding and stacking [i] based on linear OA(1622, 4096, F16, 8) (dual of [4096, 4074, 9]-code), using
(14, 14+8, 3268)-Net over F16 — Digital
Digital (14, 22, 3268)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1622, 3268, F16, 8) (dual of [3268, 3246, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(1622, 4096, F16, 8) (dual of [4096, 4074, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(1622, 4096, F16, 8) (dual of [4096, 4074, 9]-code), using
(14, 14+8, 618899)-Net in Base 16 — Upper bound on s
There is no (14, 22, 618900)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 309 485769 229053 224589 175876 > 1622 [i]