Best Known (92, 92+26, s)-Nets in Base 16
(92, 92+26, 10120)-Net over F16 — Constructive and digital
Digital (92, 118, 10120)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (3, 16, 38)-net over F16, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- digital (76, 102, 10082)-net over F16, using
- net defined by OOA [i] based on linear OOA(16102, 10082, F16, 26, 26) (dual of [(10082, 26), 262030, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(16102, 131066, F16, 26) (dual of [131066, 130964, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(16102, 131072, F16, 26) (dual of [131072, 130970, 27]-code), using
- trace code [i] based on linear OA(25651, 65536, F256, 26) (dual of [65536, 65485, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- trace code [i] based on linear OA(25651, 65536, F256, 26) (dual of [65536, 65485, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(16102, 131072, F16, 26) (dual of [131072, 130970, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(16102, 131066, F16, 26) (dual of [131066, 130964, 27]-code), using
- net defined by OOA [i] based on linear OOA(16102, 10082, F16, 26, 26) (dual of [(10082, 26), 262030, 27]-NRT-code), using
- digital (3, 16, 38)-net over F16, using
(92, 92+26, 20165)-Net in Base 16 — Constructive
(92, 118, 20165)-net in base 16, using
- 1 times m-reduction [i] based on (92, 119, 20165)-net in base 16, using
- net defined by OOA [i] based on OOA(16119, 20165, S16, 27, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(16119, 262146, S16, 27), using
- discarding factors based on OA(16119, 262147, S16, 27), using
- discarding parts of the base [i] based on linear OA(6479, 262147, F64, 27) (dual of [262147, 262068, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(6479, 262144, F64, 27) (dual of [262144, 262065, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(6476, 262144, F64, 26) (dual of [262144, 262068, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- discarding parts of the base [i] based on linear OA(6479, 262147, F64, 27) (dual of [262147, 262068, 28]-code), using
- discarding factors based on OA(16119, 262147, S16, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(16119, 262146, S16, 27), using
- net defined by OOA [i] based on OOA(16119, 20165, S16, 27, 27), using
(92, 92+26, 327339)-Net over F16 — Digital
Digital (92, 118, 327339)-net over F16, using
(92, 92+26, large)-Net in Base 16 — Upper bound on s
There is no (92, 118, large)-net in base 16, because
- 24 times m-reduction [i] would yield (92, 94, large)-net in base 16, but