Best Known (26, 32, s)-Nets in Base 8
(26, 32, 174764)-Net over F8 — Constructive and digital
Digital (26, 32, 174764)-net over F8, using
- net defined by OOA [i] based on linear OOA(832, 174764, F8, 6, 6) (dual of [(174764, 6), 1048552, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(832, 524292, F8, 6) (dual of [524292, 524260, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(832, 524294, F8, 6) (dual of [524294, 524262, 7]-code), using
- trace code [i] based on linear OA(6416, 262147, F64, 6) (dual of [262147, 262131, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- 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(6413, 262144, F64, 5) (dual of [262144, 262131, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(5) ⊂ Ce(4) [i] based on
- trace code [i] based on linear OA(6416, 262147, F64, 6) (dual of [262147, 262131, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(832, 524294, F8, 6) (dual of [524294, 524262, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(832, 524292, F8, 6) (dual of [524292, 524260, 7]-code), using
(26, 32, 524294)-Net over F8 — Digital
Digital (26, 32, 524294)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(832, 524294, F8, 6) (dual of [524294, 524262, 7]-code), using
- trace code [i] based on linear OA(6416, 262147, F64, 6) (dual of [262147, 262131, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- 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(6413, 262144, F64, 5) (dual of [262144, 262131, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(5) ⊂ Ce(4) [i] based on
- trace code [i] based on linear OA(6416, 262147, F64, 6) (dual of [262147, 262131, 7]-code), using
(26, 32, large)-Net in Base 8 — Upper bound on s
There is no (26, 32, large)-net in base 8, because
- 4 times m-reduction [i] would yield (26, 28, large)-net in base 8, but