Best Known (135−30, 135, s)-Nets in Base 8
(135−30, 135, 2186)-Net over F8 — Constructive and digital
Digital (105, 135, 2186)-net over F8, using
- net defined by OOA [i] based on linear OOA(8135, 2186, F8, 30, 30) (dual of [(2186, 30), 65445, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(8135, 32790, F8, 30) (dual of [32790, 32655, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(8135, 32792, F8, 30) (dual of [32792, 32657, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(25) [i] based on
- linear OA(8131, 32768, F8, 30) (dual of [32768, 32637, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(8111, 32768, F8, 26) (dual of [32768, 32657, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(84, 24, F8, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,8)), using
- construction X applied to Ce(29) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(8135, 32792, F8, 30) (dual of [32792, 32657, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(8135, 32790, F8, 30) (dual of [32790, 32655, 31]-code), using
(135−30, 135, 32792)-Net over F8 — Digital
Digital (105, 135, 32792)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8135, 32792, F8, 30) (dual of [32792, 32657, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(25) [i] based on
- linear OA(8131, 32768, F8, 30) (dual of [32768, 32637, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(8111, 32768, F8, 26) (dual of [32768, 32657, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(84, 24, F8, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,8)), using
- construction X applied to Ce(29) ⊂ Ce(25) [i] based on
(135−30, 135, large)-Net in Base 8 — Upper bound on s
There is no (105, 135, large)-net in base 8, because
- 28 times m-reduction [i] would yield (105, 107, large)-net in base 8, but