Best Known (90, 90+20, s)-Nets in Base 8
(90, 90+20, 26218)-Net over F8 — Constructive and digital
Digital (90, 110, 26218)-net over F8, using
- net defined by OOA [i] based on linear OOA(8110, 26218, F8, 20, 20) (dual of [(26218, 20), 524250, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(8110, 262180, F8, 20) (dual of [262180, 262070, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(8110, 262181, F8, 20) (dual of [262181, 262071, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- linear OA(8103, 262144, F8, 20) (dual of [262144, 262041, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(873, 262144, F8, 14) (dual of [262144, 262071, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(87, 37, F8, 5) (dual of [37, 30, 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(19) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(8110, 262181, F8, 20) (dual of [262181, 262071, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(8110, 262180, F8, 20) (dual of [262180, 262070, 21]-code), using
(90, 90+20, 262181)-Net over F8 — Digital
Digital (90, 110, 262181)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8110, 262181, F8, 20) (dual of [262181, 262071, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- linear OA(8103, 262144, F8, 20) (dual of [262144, 262041, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(873, 262144, F8, 14) (dual of [262144, 262071, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(87, 37, F8, 5) (dual of [37, 30, 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(19) ⊂ Ce(13) [i] based on
(90, 90+20, large)-Net in Base 8 — Upper bound on s
There is no (90, 110, large)-net in base 8, because
- 18 times m-reduction [i] would yield (90, 92, large)-net in base 8, but