Best Known (90, 90+27, s)-Nets in Base 8
(90, 90+27, 2521)-Net over F8 — Constructive and digital
Digital (90, 117, 2521)-net over F8, using
- net defined by OOA [i] based on linear OOA(8117, 2521, F8, 27, 27) (dual of [(2521, 27), 67950, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8117, 32774, F8, 27) (dual of [32774, 32657, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(8117, 32779, F8, 27) (dual of [32779, 32662, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- linear OA(8116, 32768, F8, 27) (dual of [32768, 32652, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(26) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(8117, 32779, F8, 27) (dual of [32779, 32662, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8117, 32774, F8, 27) (dual of [32774, 32657, 28]-code), using
(90, 90+27, 22520)-Net over F8 — Digital
Digital (90, 117, 22520)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8117, 22520, F8, 27) (dual of [22520, 22403, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(8117, 32779, F8, 27) (dual of [32779, 32662, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- linear OA(8116, 32768, F8, 27) (dual of [32768, 32652, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(26) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(8117, 32779, F8, 27) (dual of [32779, 32662, 28]-code), using
(90, 90+27, large)-Net in Base 8 — Upper bound on s
There is no (90, 117, large)-net in base 8, because
- 25 times m-reduction [i] would yield (90, 92, large)-net in base 8, but