Best Known (163−36, 163, s)-Nets in Base 8
(163−36, 163, 1822)-Net over F8 — Constructive and digital
Digital (127, 163, 1822)-net over F8, using
- net defined by OOA [i] based on linear OOA(8163, 1822, F8, 36, 36) (dual of [(1822, 36), 65429, 37]-NRT-code), using
- OA 18-folding and stacking [i] based on linear OA(8163, 32796, F8, 36) (dual of [32796, 32633, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(8163, 32800, F8, 36) (dual of [32800, 32637, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(29) [i] based on
- linear OA(8156, 32768, F8, 36) (dual of [32768, 32612, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- 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(87, 32, F8, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(35) ⊂ Ce(29) [i] based on
- discarding factors / shortening the dual code based on linear OA(8163, 32800, F8, 36) (dual of [32800, 32637, 37]-code), using
- OA 18-folding and stacking [i] based on linear OA(8163, 32796, F8, 36) (dual of [32796, 32633, 37]-code), using
(163−36, 163, 32800)-Net over F8 — Digital
Digital (127, 163, 32800)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8163, 32800, F8, 36) (dual of [32800, 32637, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(29) [i] based on
- linear OA(8156, 32768, F8, 36) (dual of [32768, 32612, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- 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(87, 32, F8, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(35) ⊂ Ce(29) [i] based on
(163−36, 163, large)-Net in Base 8 — Upper bound on s
There is no (127, 163, large)-net in base 8, because
- 34 times m-reduction [i] would yield (127, 129, large)-net in base 8, but