Best Known (94, 94+22, s)-Nets in Base 8
(94, 94+22, 23832)-Net over F8 — Constructive and digital
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
(94, 94+22, 184905)-Net over F8 — Digital
Digital (94, 116, 184905)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8116, 184905, F8, 22) (dual of [184905, 184789, 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
(94, 94+22, large)-Net in Base 8 — Upper bound on s
There is no (94, 116, large)-net in base 8, because
- 20 times m-reduction [i] would yield (94, 96, large)-net in base 8, but