Best Known (95, 123, s)-Nets in Base 16
(95, 123, 9365)-Net over F16 — Constructive and digital
Digital (95, 123, 9365)-net over F16, using
- 161 times duplication [i] based on digital (94, 122, 9365)-net over F16, using
- net defined by OOA [i] based on linear OOA(16122, 9365, F16, 28, 28) (dual of [(9365, 28), 262098, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(16122, 131110, F16, 28) (dual of [131110, 130988, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(16122, 131112, F16, 28) (dual of [131112, 130990, 29]-code), using
- trace code [i] based on linear OA(25661, 65556, F256, 28) (dual of [65556, 65495, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(20) [i] based on
- linear OA(25655, 65536, F256, 28) (dual of [65536, 65481, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2566, 20, F256, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,256)), using
- discarding factors / shortening the dual code based on linear OA(2566, 256, F256, 6) (dual of [256, 250, 7]-code or 256-arc in PG(5,256)), using
- Reed–Solomon code RS(250,256) [i]
- discarding factors / shortening the dual code based on linear OA(2566, 256, F256, 6) (dual of [256, 250, 7]-code or 256-arc in PG(5,256)), using
- construction X applied to Ce(27) ⊂ Ce(20) [i] based on
- trace code [i] based on linear OA(25661, 65556, F256, 28) (dual of [65556, 65495, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(16122, 131112, F16, 28) (dual of [131112, 130990, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(16122, 131110, F16, 28) (dual of [131110, 130988, 29]-code), using
- net defined by OOA [i] based on linear OOA(16122, 9365, F16, 28, 28) (dual of [(9365, 28), 262098, 29]-NRT-code), using
(95, 123, 18724)-Net in Base 16 — Constructive
(95, 123, 18724)-net in base 16, using
- base change [i] based on digital (54, 82, 18724)-net over F64, using
- net defined by OOA [i] based on linear OOA(6482, 18724, F64, 28, 28) (dual of [(18724, 28), 524190, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(6482, 262136, F64, 28) (dual of [262136, 262054, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(6482, 262144, F64, 28) (dual of [262144, 262062, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(6482, 262144, F64, 28) (dual of [262144, 262062, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(6482, 262136, F64, 28) (dual of [262136, 262054, 29]-code), using
- net defined by OOA [i] based on linear OOA(6482, 18724, F64, 28, 28) (dual of [(18724, 28), 524190, 29]-NRT-code), using
(95, 123, 222729)-Net over F16 — Digital
Digital (95, 123, 222729)-net over F16, using
(95, 123, large)-Net in Base 16 — Upper bound on s
There is no (95, 123, large)-net in base 16, because
- 26 times m-reduction [i] would yield (95, 97, large)-net in base 16, but