Best Known (108, 108+22, s)-Nets in Base 8
(108, 108+22, 47663)-Net over F8 — Constructive and digital
Digital (108, 130, 47663)-net over F8, using
- 82 times duplication [i] based on digital (106, 128, 47663)-net over F8, using
- net defined by OOA [i] based on linear OOA(8128, 47663, F8, 22, 22) (dual of [(47663, 22), 1048458, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(8128, 524293, F8, 22) (dual of [524293, 524165, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(8128, 524294, F8, 22) (dual of [524294, 524166, 23]-code), using
- trace code [i] based on linear OA(6464, 262147, F64, 22) (dual of [262147, 262083, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(6464, 262144, F64, 22) (dual of [262144, 262080, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(6461, 262144, F64, 21) (dual of [262144, 262083, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(21) ⊂ Ce(20) [i] based on
- trace code [i] based on linear OA(6464, 262147, F64, 22) (dual of [262147, 262083, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(8128, 524294, F8, 22) (dual of [524294, 524166, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(8128, 524293, F8, 22) (dual of [524293, 524165, 23]-code), using
- net defined by OOA [i] based on linear OOA(8128, 47663, F8, 22, 22) (dual of [(47663, 22), 1048458, 23]-NRT-code), using
(108, 108+22, 524302)-Net over F8 — Digital
Digital (108, 130, 524302)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8130, 524302, F8, 22) (dual of [524302, 524172, 23]-code), using
- trace code [i] based on linear OA(6465, 262151, F64, 22) (dual of [262151, 262086, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(6464, 262144, F64, 22) (dual of [262144, 262080, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(6458, 262144, F64, 20) (dual of [262144, 262086, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- trace code [i] based on linear OA(6465, 262151, F64, 22) (dual of [262151, 262086, 23]-code), using
(108, 108+22, large)-Net in Base 8 — Upper bound on s
There is no (108, 130, large)-net in base 8, because
- 20 times m-reduction [i] would yield (108, 110, large)-net in base 8, but