Best Known (92, 124, s)-Nets in Base 16
(92, 124, 4097)-Net over F16 — Constructive and digital
Digital (92, 124, 4097)-net over F16, using
- net defined by OOA [i] based on linear OOA(16124, 4097, F16, 32, 32) (dual of [(4097, 32), 130980, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(16124, 65552, F16, 32) (dual of [65552, 65428, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(16124, 65554, F16, 32) (dual of [65554, 65430, 33]-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(163, 18, F16, 3) (dual of [18, 15, 4]-code or 18-arc in PG(2,16) or 18-cap in PG(2,16)), using
- construction X applied to Ce(32) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(16124, 65554, F16, 32) (dual of [65554, 65430, 33]-code), using
- OA 16-folding and stacking [i] based on linear OA(16124, 65552, F16, 32) (dual of [65552, 65428, 33]-code), using
(92, 124, 65554)-Net over F16 — Digital
Digital (92, 124, 65554)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16124, 65554, F16, 32) (dual of [65554, 65430, 33]-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(163, 18, F16, 3) (dual of [18, 15, 4]-code or 18-arc in PG(2,16) or 18-cap in PG(2,16)), using
- construction X applied to Ce(32) ⊂ Ce(27) [i] based on
(92, 124, large)-Net in Base 16 — Upper bound on s
There is no (92, 124, large)-net in base 16, because
- 30 times m-reduction [i] would yield (92, 94, large)-net in base 16, but