Best Known (35, 42, s)-Nets in Base 8
(35, 42, 174829)-Net over F8 — Constructive and digital
Digital (35, 42, 174829)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (1, 4, 65)-net over F8, using
- net defined by OOA [i] based on linear OOA(84, 65, F8, 3, 3) (dual of [(65, 3), 191, 4]-NRT-code), using
- digital (31, 38, 174764)-net over F8, using
- net defined by OOA [i] based on linear OOA(838, 174764, F8, 7, 7) (dual of [(174764, 7), 1223310, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(838, 524293, F8, 7) (dual of [524293, 524255, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(838, 524294, F8, 7) (dual of [524294, 524256, 8]-code), using
- trace code [i] based on linear OA(6419, 262147, F64, 7) (dual of [262147, 262128, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(6419, 262144, F64, 7) (dual of [262144, 262125, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(6416, 262144, F64, 6) (dual of [262144, 262128, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- trace code [i] based on linear OA(6419, 262147, F64, 7) (dual of [262147, 262128, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(838, 524294, F8, 7) (dual of [524294, 524256, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(838, 524293, F8, 7) (dual of [524293, 524255, 8]-code), using
- net defined by OOA [i] based on linear OOA(838, 174764, F8, 7, 7) (dual of [(174764, 7), 1223310, 8]-NRT-code), using
- digital (1, 4, 65)-net over F8, using
(35, 42, 349526)-Net in Base 8 — Constructive
(35, 42, 349526)-net in base 8, using
- net defined by OOA [i] based on OOA(842, 349526, S8, 7, 7), using
- OOA 3-folding and stacking with additional row [i] based on OA(842, 1048579, S8, 7), using
- discarding factors based on OA(842, 1048581, S8, 7), using
- discarding parts of the base [i] based on linear OA(1631, 1048581, F16, 7) (dual of [1048581, 1048550, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(1631, 1048576, F16, 7) (dual of [1048576, 1048545, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(1626, 1048576, F16, 6) (dual of [1048576, 1048550, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(160, 5, F16, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- discarding parts of the base [i] based on linear OA(1631, 1048581, F16, 7) (dual of [1048581, 1048550, 8]-code), using
- discarding factors based on OA(842, 1048581, S8, 7), using
- OOA 3-folding and stacking with additional row [i] based on OA(842, 1048579, S8, 7), using
(35, 42, 896923)-Net over F8 — Digital
Digital (35, 42, 896923)-net over F8, using
(35, 42, large)-Net in Base 8 — Upper bound on s
There is no (35, 42, large)-net in base 8, because
- 5 times m-reduction [i] would yield (35, 37, large)-net in base 8, but