Best Known (75, 75+23, s)-Nets in Base 16
(75, 75+23, 11918)-Net over F16 — Constructive and digital
Digital (75, 98, 11918)-net over F16, using
- net defined by OOA [i] based on linear OOA(1698, 11918, F16, 23, 23) (dual of [(11918, 23), 274016, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(1698, 131099, F16, 23) (dual of [131099, 131001, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(1698, 131100, F16, 23) (dual of [131100, 131002, 24]-code), using
- trace code [i] based on linear OA(25649, 65550, F256, 23) (dual of [65550, 65501, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
- linear OA(25645, 65536, F256, 23) (dual of [65536, 65491, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(22) ⊂ Ce(17) [i] based on
- trace code [i] based on linear OA(25649, 65550, F256, 23) (dual of [65550, 65501, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(1698, 131100, F16, 23) (dual of [131100, 131002, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(1698, 131099, F16, 23) (dual of [131099, 131001, 24]-code), using
(75, 75+23, 139509)-Net over F16 — Digital
Digital (75, 98, 139509)-net over F16, using
(75, 75+23, large)-Net in Base 16 — Upper bound on s
There is no (75, 98, large)-net in base 16, because
- 21 times m-reduction [i] would yield (75, 77, large)-net in base 16, but