Best Known (126, 126+26, s)-Nets in Base 8
(126, 126+26, 40330)-Net over F8 — Constructive and digital
Digital (126, 152, 40330)-net over F8, using
- net defined by OOA [i] based on linear OOA(8152, 40330, F8, 26, 26) (dual of [(40330, 26), 1048428, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(8152, 524290, F8, 26) (dual of [524290, 524138, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(8152, 524294, F8, 26) (dual of [524294, 524142, 27]-code), using
- trace code [i] based on linear OA(6476, 262147, F64, 26) (dual of [262147, 262071, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(6476, 262144, F64, 26) (dual of [262144, 262068, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(6473, 262144, F64, 25) (dual of [262144, 262071, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(25) ⊂ Ce(24) [i] based on
- trace code [i] based on linear OA(6476, 262147, F64, 26) (dual of [262147, 262071, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(8152, 524294, F8, 26) (dual of [524294, 524142, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(8152, 524290, F8, 26) (dual of [524290, 524138, 27]-code), using
(126, 126+26, 524294)-Net over F8 — Digital
Digital (126, 152, 524294)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8152, 524294, F8, 26) (dual of [524294, 524142, 27]-code), using
- trace code [i] based on linear OA(6476, 262147, F64, 26) (dual of [262147, 262071, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(6476, 262144, F64, 26) (dual of [262144, 262068, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(6473, 262144, F64, 25) (dual of [262144, 262071, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(25) ⊂ Ce(24) [i] based on
- trace code [i] based on linear OA(6476, 262147, F64, 26) (dual of [262147, 262071, 27]-code), using
(126, 126+26, large)-Net in Base 8 — Upper bound on s
There is no (126, 152, large)-net in base 8, because
- 24 times m-reduction [i] would yield (126, 128, large)-net in base 8, but