Best Known (133, 133+38, s)-Nets in Base 8
(133, 133+38, 1726)-Net over F8 — Constructive and digital
Digital (133, 171, 1726)-net over F8, using
- net defined by OOA [i] based on linear OOA(8171, 1726, F8, 38, 38) (dual of [(1726, 38), 65417, 39]-NRT-code), using
- OA 19-folding and stacking [i] based on linear OA(8171, 32794, F8, 38) (dual of [32794, 32623, 39]-code), using
- construction XX applied to Ce(37) ⊂ Ce(33) ⊂ Ce(32) [i] based on
- linear OA(8166, 32768, F8, 38) (dual of [32768, 32602, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(8146, 32768, F8, 34) (dual of [32768, 32622, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(8141, 32768, F8, 33) (dual of [32768, 32627, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(84, 25, F8, 3) (dual of [25, 21, 4]-code or 25-cap in PG(3,8)), 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(37) ⊂ Ce(33) ⊂ Ce(32) [i] based on
- OA 19-folding and stacking [i] based on linear OA(8171, 32794, F8, 38) (dual of [32794, 32623, 39]-code), using
(133, 133+38, 32794)-Net over F8 — Digital
Digital (133, 171, 32794)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8171, 32794, F8, 38) (dual of [32794, 32623, 39]-code), using
- construction XX applied to Ce(37) ⊂ Ce(33) ⊂ Ce(32) [i] based on
- linear OA(8166, 32768, F8, 38) (dual of [32768, 32602, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(8146, 32768, F8, 34) (dual of [32768, 32622, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(8141, 32768, F8, 33) (dual of [32768, 32627, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(84, 25, F8, 3) (dual of [25, 21, 4]-code or 25-cap in PG(3,8)), 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(37) ⊂ Ce(33) ⊂ Ce(32) [i] based on
(133, 133+38, large)-Net in Base 8 — Upper bound on s
There is no (133, 171, large)-net in base 8, because
- 36 times m-reduction [i] would yield (133, 135, large)-net in base 8, but