Best Known (95, 95+22, s)-Nets in Base 8
(95, 95+22, 23832)-Net over F8 — Constructive and digital
Digital (95, 117, 23832)-net over F8, using
- 81 times duplication [i] based on digital (94, 116, 23832)-net over F8, using
- net defined by OOA [i] based on linear OOA(8116, 23832, F8, 22, 22) (dual of [(23832, 22), 524188, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(8116, 262152, F8, 22) (dual of [262152, 262036, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(8116, 262157, F8, 22) (dual of [262157, 262041, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(8115, 262144, F8, 22) (dual of [262144, 262029, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(8103, 262144, F8, 20) (dual of [262144, 262041, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(81, 13, F8, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(8116, 262157, F8, 22) (dual of [262157, 262041, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(8116, 262152, F8, 22) (dual of [262152, 262036, 23]-code), using
- net defined by OOA [i] based on linear OOA(8116, 23832, F8, 22, 22) (dual of [(23832, 22), 524188, 23]-NRT-code), using
(95, 95+22, 205166)-Net over F8 — Digital
Digital (95, 117, 205166)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8117, 205166, F8, 22) (dual of [205166, 205049, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(8117, 262159, F8, 22) (dual of [262159, 262042, 23]-code), using
- construction XX applied to Ce(21) ⊂ Ce(19) ⊂ Ce(18) [i] based on
- linear OA(8115, 262144, F8, 22) (dual of [262144, 262029, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(8103, 262144, F8, 20) (dual of [262144, 262041, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(897, 262144, F8, 19) (dual of [262144, 262047, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(81, 14, F8, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(21) ⊂ Ce(19) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(8117, 262159, F8, 22) (dual of [262159, 262042, 23]-code), using
(95, 95+22, large)-Net in Base 8 — Upper bound on s
There is no (95, 117, large)-net in base 8, because
- 20 times m-reduction [i] would yield (95, 97, large)-net in base 8, but