Best Known (80−19, 80, s)-Nets in Base 8
(80−19, 80, 912)-Net over F8 — Constructive and digital
Digital (61, 80, 912)-net over F8, using
- 81 times duplication [i] based on digital (60, 79, 912)-net over F8, using
- net defined by OOA [i] based on linear OOA(879, 912, F8, 19, 19) (dual of [(912, 19), 17249, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(879, 8209, F8, 19) (dual of [8209, 8130, 20]-code), using
- 1 times code embedding in larger space [i] based on linear OA(878, 8208, F8, 19) (dual of [8208, 8130, 20]-code), using
- trace code [i] based on linear OA(6439, 4104, F64, 19) (dual of [4104, 4065, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(6437, 4096, F64, 19) (dual of [4096, 4059, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(642, 8, F64, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- trace code [i] based on linear OA(6439, 4104, F64, 19) (dual of [4104, 4065, 20]-code), using
- 1 times code embedding in larger space [i] based on linear OA(878, 8208, F8, 19) (dual of [8208, 8130, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(879, 8209, F8, 19) (dual of [8209, 8130, 20]-code), using
- net defined by OOA [i] based on linear OOA(879, 912, F8, 19, 19) (dual of [(912, 19), 17249, 20]-NRT-code), using
(80−19, 80, 1032)-Net in Base 8 — Constructive
(61, 80, 1032)-net in base 8, using
- base change [i] based on digital (41, 60, 1032)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (11, 20, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 10, 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, 10, 258)-net over F256, using
- digital (21, 40, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 20, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256 (see above)
- trace code for nets [i] based on digital (1, 20, 258)-net over F256, using
- digital (11, 20, 516)-net over F16, using
- (u, u+v)-construction [i] based on
(80−19, 80, 11146)-Net over F8 — Digital
Digital (61, 80, 11146)-net over F8, using
(80−19, 80, large)-Net in Base 8 — Upper bound on s
There is no (61, 80, large)-net in base 8, because
- 17 times m-reduction [i] would yield (61, 63, large)-net in base 8, but