Best Known (80, 80+24, s)-Nets in Base 16
(80, 80+24, 10925)-Net over F16 — Constructive and digital
Digital (80, 104, 10925)-net over F16, using
- 162 times duplication [i] based on digital (78, 102, 10925)-net over F16, using
- net defined by OOA [i] based on linear OOA(16102, 10925, F16, 24, 24) (dual of [(10925, 24), 262098, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(16102, 131100, F16, 24) (dual of [131100, 130998, 25]-code), using
- trace code [i] based on linear OA(25651, 65550, F256, 24) (dual of [65550, 65499, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(18) [i] based on
- linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(25637, 65536, F256, 19) (dual of [65536, 65499, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(23) ⊂ Ce(18) [i] based on
- trace code [i] based on linear OA(25651, 65550, F256, 24) (dual of [65550, 65499, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(16102, 131100, F16, 24) (dual of [131100, 130998, 25]-code), using
- net defined by OOA [i] based on linear OOA(16102, 10925, F16, 24, 24) (dual of [(10925, 24), 262098, 25]-NRT-code), using
(80, 80+24, 175029)-Net over F16 — Digital
Digital (80, 104, 175029)-net over F16, using
(80, 80+24, large)-Net in Base 16 — Upper bound on s
There is no (80, 104, large)-net in base 16, because
- 22 times m-reduction [i] would yield (80, 82, large)-net in base 16, but