Best Known (99−23, 99, s)-Nets in Base 8
(99−23, 99, 747)-Net over F8 — Constructive and digital
Digital (76, 99, 747)-net over F8, using
- 81 times duplication [i] based on digital (75, 98, 747)-net over F8, using
- net defined by OOA [i] based on linear OOA(898, 747, F8, 23, 23) (dual of [(747, 23), 17083, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(898, 8218, F8, 23) (dual of [8218, 8120, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(898, 8220, F8, 23) (dual of [8220, 8122, 24]-code), using
- trace code [i] based on linear OA(6449, 4110, F64, 23) (dual of [4110, 4061, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
- linear OA(6445, 4096, F64, 23) (dual of [4096, 4051, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(6435, 4096, F64, 18) (dual of [4096, 4061, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(22) ⊂ Ce(17) [i] based on
- trace code [i] based on linear OA(6449, 4110, F64, 23) (dual of [4110, 4061, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(898, 8220, F8, 23) (dual of [8220, 8122, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(898, 8218, F8, 23) (dual of [8218, 8120, 24]-code), using
- net defined by OOA [i] based on linear OOA(898, 747, F8, 23, 23) (dual of [(747, 23), 17083, 24]-NRT-code), using
(99−23, 99, 1032)-Net in Base 8 — Constructive
(76, 99, 1032)-net in base 8, using
- 83 times duplication [i] based on (73, 96, 1032)-net in base 8, using
- base change [i] based on digital (49, 72, 1032)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (13, 24, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 12, 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, 12, 258)-net over F256, using
- digital (25, 48, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 24, 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, 24, 258)-net over F256, using
- digital (13, 24, 516)-net over F16, using
- (u, u+v)-construction [i] based on
- base change [i] based on digital (49, 72, 1032)-net over F16, using
(99−23, 99, 14996)-Net over F8 — Digital
Digital (76, 99, 14996)-net over F8, using
(99−23, 99, large)-Net in Base 8 — Upper bound on s
There is no (76, 99, large)-net in base 8, because
- 21 times m-reduction [i] would yield (76, 78, large)-net in base 8, but