Best Known (95, 95+33, s)-Nets in Base 16
(95, 95+33, 4097)-Net over F16 — Constructive and digital
Digital (95, 128, 4097)-net over F16, using
- 163 times duplication [i] based on digital (92, 125, 4097)-net over F16, using
- net defined by OOA [i] based on linear OOA(16125, 4097, F16, 33, 33) (dual of [(4097, 33), 135076, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(16125, 65553, F16, 33) (dual of [65553, 65428, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(27) [i] based on
- linear OA(16121, 65536, F16, 33) (dual of [65536, 65415, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(16105, 65536, F16, 28) (dual of [65536, 65431, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(164, 17, F16, 4) (dual of [17, 13, 5]-code or 17-arc in PG(3,16)), using
- extended Reed–Solomon code RSe(13,16) [i]
- construction X applied to Ce(32) ⊂ Ce(27) [i] based on
- OOA 16-folding and stacking with additional row [i] based on linear OA(16125, 65553, F16, 33) (dual of [65553, 65428, 34]-code), using
- net defined by OOA [i] based on linear OOA(16125, 4097, F16, 33, 33) (dual of [(4097, 33), 135076, 34]-NRT-code), using
(95, 95+33, 65563)-Net over F16 — Digital
Digital (95, 128, 65563)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16128, 65563, F16, 33) (dual of [65563, 65435, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(26) [i] based on
- linear OA(16121, 65536, F16, 33) (dual of [65536, 65415, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(16101, 65536, F16, 27) (dual of [65536, 65435, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(167, 27, F16, 5) (dual of [27, 20, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(167, 241, F16, 5) (dual of [241, 234, 6]-code), using
- construction X applied to Ce(32) ⊂ Ce(26) [i] based on
(95, 95+33, large)-Net in Base 16 — Upper bound on s
There is no (95, 128, large)-net in base 16, because
- 31 times m-reduction [i] would yield (95, 97, large)-net in base 16, but