Best Known (89, 110, s)-Nets in Base 8
(89, 110, 26215)-Net over F8 — Constructive and digital
Digital (89, 110, 26215)-net over F8, using
- net defined by OOA [i] based on linear OOA(8110, 26215, F8, 21, 21) (dual of [(26215, 21), 550405, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(8110, 262151, F8, 21) (dual of [262151, 262041, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(8110, 262158, F8, 21) (dual of [262158, 262048, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(8109, 262145, F8, 21) (dual of [262145, 262036, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(897, 262145, F8, 19) (dual of [262145, 262048, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(81, 13, F8, 1) (dual of [13, 12, 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 C([0,10]) ⊂ C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(8110, 262158, F8, 21) (dual of [262158, 262048, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(8110, 262151, F8, 21) (dual of [262151, 262041, 22]-code), using
(89, 110, 171780)-Net over F8 — Digital
Digital (89, 110, 171780)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8110, 171780, F8, 21) (dual of [171780, 171670, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(8110, 262158, F8, 21) (dual of [262158, 262048, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(8109, 262145, F8, 21) (dual of [262145, 262036, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(897, 262145, F8, 19) (dual of [262145, 262048, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(81, 13, F8, 1) (dual of [13, 12, 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 C([0,10]) ⊂ C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(8110, 262158, F8, 21) (dual of [262158, 262048, 22]-code), using
(89, 110, large)-Net in Base 8 — Upper bound on s
There is no (89, 110, large)-net in base 8, because
- 19 times m-reduction [i] would yield (89, 91, large)-net in base 8, but