Best Known (99, 125, s)-Nets in Base 16
(99, 125, 80661)-Net over F16 — Constructive and digital
Digital (99, 125, 80661)-net over F16, using
- 162 times duplication [i] based on digital (97, 123, 80661)-net over F16, using
- net defined by OOA [i] based on linear OOA(16123, 80661, F16, 26, 26) (dual of [(80661, 26), 2097063, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(16123, 1048593, F16, 26) (dual of [1048593, 1048470, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- linear OA(16121, 1048576, F16, 26) (dual of [1048576, 1048455, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(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(25) ⊂ Ce(22) [i] based on
- OA 13-folding and stacking [i] based on linear OA(16123, 1048593, F16, 26) (dual of [1048593, 1048470, 27]-code), using
- net defined by OOA [i] based on linear OOA(16123, 80661, F16, 26, 26) (dual of [(80661, 26), 2097063, 27]-NRT-code), using
(99, 125, 1048600)-Net over F16 — Digital
Digital (99, 125, 1048600)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16125, 1048600, F16, 26) (dual of [1048600, 1048475, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(16121, 1048576, F16, 26) (dual of [1048576, 1048455, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(164, 24, F16, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,16)), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
(99, 125, large)-Net in Base 16 — Upper bound on s
There is no (99, 125, large)-net in base 16, because
- 24 times m-reduction [i] would yield (99, 101, large)-net in base 16, but