Best Known (132−30, 132, s)-Nets in Base 8
(132−30, 132, 2185)-Net over F8 — Constructive and digital
Digital (102, 132, 2185)-net over F8, using
- net defined by OOA [i] based on linear OOA(8132, 2185, F8, 30, 30) (dual of [(2185, 30), 65418, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(8132, 32775, F8, 30) (dual of [32775, 32643, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(8132, 32779, F8, 30) (dual of [32779, 32647, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(27) [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(8121, 32768, F8, 28) (dual of [32768, 32647, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(81, 11, F8, 1) (dual of [11, 10, 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(29) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(8132, 32779, F8, 30) (dual of [32779, 32647, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(8132, 32775, F8, 30) (dual of [32775, 32643, 31]-code), using
(132−30, 132, 27090)-Net over F8 — Digital
Digital (102, 132, 27090)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8132, 27090, F8, 30) (dual of [27090, 26958, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(8132, 32779, F8, 30) (dual of [32779, 32647, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(27) [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(8121, 32768, F8, 28) (dual of [32768, 32647, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(81, 11, F8, 1) (dual of [11, 10, 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(29) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(8132, 32779, F8, 30) (dual of [32779, 32647, 31]-code), using
(132−30, 132, large)-Net in Base 8 — Upper bound on s
There is no (102, 132, large)-net in base 8, because
- 28 times m-reduction [i] would yield (102, 104, large)-net in base 8, but