Best Known (94, 94+25, s)-Nets in Base 16
(94, 94+25, 87382)-Net over F16 — Constructive and digital
Digital (94, 119, 87382)-net over F16, using
- 162 times duplication [i] based on digital (92, 117, 87382)-net over F16, using
- net defined by OOA [i] based on linear OOA(16117, 87382, F16, 25, 25) (dual of [(87382, 25), 2184433, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(16117, 1048585, F16, 25) (dual of [1048585, 1048468, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(16117, 1048587, F16, 25) (dual of [1048587, 1048470, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(16116, 1048576, F16, 25) (dual of [1048576, 1048460, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(16106, 1048576, F16, 23) (dual of [1048576, 1048470, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(161, 11, F16, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(16117, 1048587, F16, 25) (dual of [1048587, 1048470, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(16117, 1048585, F16, 25) (dual of [1048585, 1048468, 26]-code), using
- net defined by OOA [i] based on linear OOA(16117, 87382, F16, 25, 25) (dual of [(87382, 25), 2184433, 26]-NRT-code), using
(94, 94+25, 946278)-Net over F16 — Digital
Digital (94, 119, 946278)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16119, 946278, F16, 25) (dual of [946278, 946159, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(16119, 1048594, F16, 25) (dual of [1048594, 1048475, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(16118, 1048593, F16, 25) (dual of [1048593, 1048475, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(16116, 1048576, F16, 25) (dual of [1048576, 1048460, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(16101, 1048576, F16, 22) (dual of [1048576, 1048475, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(162, 17, F16, 2) (dual of [17, 15, 3]-code or 17-arc in PG(1,16)), using
- extended Reed–Solomon code RSe(15,16) [i]
- Hamming code H(2,16) [i]
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(16118, 1048593, F16, 25) (dual of [1048593, 1048475, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(16119, 1048594, F16, 25) (dual of [1048594, 1048475, 26]-code), using
(94, 94+25, large)-Net in Base 16 — Upper bound on s
There is no (94, 119, large)-net in base 16, because
- 23 times m-reduction [i] would yield (94, 96, large)-net in base 16, but