Best Known (94−22, 94, s)-Nets in Base 16
(94−22, 94, 11918)-Net over F16 — Constructive and digital
Digital (72, 94, 11918)-net over F16, using
- net defined by OOA [i] based on linear OOA(1694, 11918, F16, 22, 22) (dual of [(11918, 22), 262102, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(1694, 131098, F16, 22) (dual of [131098, 131004, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(1694, 131100, F16, 22) (dual of [131100, 131006, 23]-code), using
- trace code [i] based on linear OA(25647, 65550, F256, 22) (dual of [65550, 65503, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(25633, 65536, F256, 17) (dual of [65536, 65503, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2564, 14, F256, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,256)), using
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- Reed–Solomon code RS(252,256) [i]
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- trace code [i] based on linear OA(25647, 65550, F256, 22) (dual of [65550, 65503, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(1694, 131100, F16, 22) (dual of [131100, 131006, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(1694, 131098, F16, 22) (dual of [131098, 131004, 23]-code), using
(94−22, 94, 142005)-Net over F16 — Digital
Digital (72, 94, 142005)-net over F16, using
(94−22, 94, large)-Net in Base 16 — Upper bound on s
There is no (72, 94, large)-net in base 16, because
- 20 times m-reduction [i] would yield (72, 74, large)-net in base 16, but