Best Known (72, 72+22, s)-Nets in Base 8
(72, 72+22, 747)-Net over F8 — Constructive and digital
Digital (72, 94, 747)-net over F8, using
- net defined by OOA [i] based on linear OOA(894, 747, F8, 22, 22) (dual of [(747, 22), 16340, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(894, 8217, F8, 22) (dual of [8217, 8123, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(894, 8220, F8, 22) (dual of [8220, 8126, 23]-code), using
- trace code [i] based on linear OA(6447, 4110, F64, 22) (dual of [4110, 4063, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(6443, 4096, F64, 22) (dual of [4096, 4053, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(6433, 4096, F64, 17) (dual of [4096, 4063, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(644, 14, F64, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,64)), using
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- Reed–Solomon code RS(60,64) [i]
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- trace code [i] based on linear OA(6447, 4110, F64, 22) (dual of [4110, 4063, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(894, 8220, F8, 22) (dual of [8220, 8126, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(894, 8217, F8, 22) (dual of [8217, 8123, 23]-code), using
(72, 72+22, 1032)-Net in Base 8 — Constructive
(72, 94, 1032)-net in base 8, using
- trace code for nets [i] based on (25, 47, 516)-net in base 64, using
- 1 times m-reduction [i] based on (25, 48, 516)-net in base 64, using
- base change [i] based on digital (13, 36, 516)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (1, 24, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256 (see above)
- digital (1, 12, 258)-net over F256, using
- (u, u+v)-construction [i] based on
- base change [i] based on digital (13, 36, 516)-net over F256, using
- 1 times m-reduction [i] based on (25, 48, 516)-net in base 64, using
(72, 72+22, 13681)-Net over F8 — Digital
Digital (72, 94, 13681)-net over F8, using
(72, 72+22, large)-Net in Base 8 — Upper bound on s
There is no (72, 94, large)-net in base 8, because
- 20 times m-reduction [i] would yield (72, 74, large)-net in base 8, but