Best Known (93, 119, s)-Nets in Base 16
(93, 119, 10127)-Net over F16 — Constructive and digital
Digital (93, 119, 10127)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (4, 17, 45)-net over F16, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 4 and N(F) ≥ 45, using
- net from sequence [i] based on digital (4, 44)-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 (4, 17, 45)-net over F16, using
(93, 119, 20166)-Net in Base 16 — Constructive
(93, 119, 20166)-net in base 16, using
- net defined by OOA [i] based on OOA(16119, 20166, S16, 26, 26), using
- OA 13-folding and stacking [i] based on OA(16119, 262158, S16, 26), using
- discarding factors based on OA(16119, 262159, S16, 26), using
- discarding parts of the base [i] based on linear OA(6479, 262159, F64, 26) (dual of [262159, 262080, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- 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(6464, 262144, F64, 22) (dual of [262144, 262080, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(643, 15, F64, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,64) or 15-cap in PG(2,64)), using
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- Reed–Solomon code RS(61,64) [i]
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- discarding parts of the base [i] based on linear OA(6479, 262159, F64, 26) (dual of [262159, 262080, 27]-code), using
- discarding factors based on OA(16119, 262159, S16, 26), using
- OA 13-folding and stacking [i] based on OA(16119, 262158, S16, 26), using
(93, 119, 365730)-Net over F16 — Digital
Digital (93, 119, 365730)-net over F16, using
(93, 119, large)-Net in Base 16 — Upper bound on s
There is no (93, 119, large)-net in base 16, because
- 24 times m-reduction [i] would yield (93, 95, large)-net in base 16, but