Best Known (75, 96, s)-Nets in Base 16
(75, 96, 104858)-Net over F16 — Constructive and digital
Digital (75, 96, 104858)-net over F16, using
- net defined by OOA [i] based on linear OOA(1696, 104858, F16, 21, 21) (dual of [(104858, 21), 2201922, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(1696, 1048581, F16, 21) (dual of [1048581, 1048485, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(1696, 1048576, F16, 21) (dual of [1048576, 1048480, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(1691, 1048576, F16, 20) (dual of [1048576, 1048485, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(160, 5, F16, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- OOA 10-folding and stacking with additional row [i] based on linear OA(1696, 1048581, F16, 21) (dual of [1048581, 1048485, 22]-code), using
(75, 96, 554264)-Net over F16 — Digital
Digital (75, 96, 554264)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1696, 554264, F16, 21) (dual of [554264, 554168, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(1696, 1048576, F16, 21) (dual of [1048576, 1048480, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(1696, 1048576, F16, 21) (dual of [1048576, 1048480, 22]-code), using
(75, 96, large)-Net in Base 16 — Upper bound on s
There is no (75, 96, large)-net in base 16, because
- 19 times m-reduction [i] would yield (75, 77, large)-net in base 16, but