Best Known (65, 65+20, s)-Nets in Base 8
(65, 65+20, 821)-Net over F8 — Constructive and digital
Digital (65, 85, 821)-net over F8, using
- 81 times duplication [i] based on digital (64, 84, 821)-net over F8, using
- net defined by OOA [i] based on linear OOA(884, 821, F8, 20, 20) (dual of [(821, 20), 16336, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(884, 8210, F8, 20) (dual of [8210, 8126, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(884, 8214, F8, 20) (dual of [8214, 8130, 21]-code), using
- trace code [i] based on linear OA(6442, 4107, F64, 20) (dual of [4107, 4065, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(15) [i] based on
- linear OA(6439, 4096, F64, 20) (dual of [4096, 4057, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(6431, 4096, F64, 16) (dual of [4096, 4065, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(643, 11, F64, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,64) or 11-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(19) ⊂ Ce(15) [i] based on
- trace code [i] based on linear OA(6442, 4107, F64, 20) (dual of [4107, 4065, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(884, 8214, F8, 20) (dual of [8214, 8130, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(884, 8210, F8, 20) (dual of [8210, 8126, 21]-code), using
- net defined by OOA [i] based on linear OOA(884, 821, F8, 20, 20) (dual of [(821, 20), 16336, 21]-NRT-code), using
(65, 65+20, 1030)-Net in Base 8 — Constructive
(65, 85, 1030)-net in base 8, using
- 81 times duplication [i] based on (64, 84, 1030)-net in base 8, using
- base change [i] based on digital (43, 63, 1030)-net over F16, using
- 1 times m-reduction [i] based on digital (43, 64, 1030)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (10, 20, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 10, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 10, 257)-net over F256, using
- digital (23, 44, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 22, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- trace code for nets [i] based on digital (1, 22, 258)-net over F256, using
- digital (10, 20, 514)-net over F16, using
- (u, u+v)-construction [i] based on
- 1 times m-reduction [i] based on digital (43, 64, 1030)-net over F16, using
- base change [i] based on digital (43, 63, 1030)-net over F16, using
(65, 65+20, 12433)-Net over F8 — Digital
Digital (65, 85, 12433)-net over F8, using
(65, 65+20, large)-Net in Base 8 — Upper bound on s
There is no (65, 85, large)-net in base 8, because
- 18 times m-reduction [i] would yield (65, 67, large)-net in base 8, but