Best Known (88, 88+17, s)-Nets in Base 8
(88, 88+17, 262148)-Net over F8 — Constructive and digital
Digital (88, 105, 262148)-net over F8, using
- net defined by OOA [i] based on linear OOA(8105, 262148, F8, 17, 17) (dual of [(262148, 17), 4456411, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(8105, 2097185, F8, 17) (dual of [2097185, 2097080, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(8105, 2097186, F8, 17) (dual of [2097186, 2097081, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- linear OA(899, 2097152, F8, 17) (dual of [2097152, 2097053, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(871, 2097152, F8, 12) (dual of [2097152, 2097081, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(86, 34, F8, 4) (dual of [34, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- 1 times truncation [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(8105, 2097186, F8, 17) (dual of [2097186, 2097081, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(8105, 2097185, F8, 17) (dual of [2097185, 2097080, 18]-code), using
(88, 88+17, 1675291)-Net over F8 — Digital
Digital (88, 105, 1675291)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8105, 1675291, F8, 17) (dual of [1675291, 1675186, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(8105, 2097186, F8, 17) (dual of [2097186, 2097081, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- linear OA(899, 2097152, F8, 17) (dual of [2097152, 2097053, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(871, 2097152, F8, 12) (dual of [2097152, 2097081, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(86, 34, F8, 4) (dual of [34, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- 1 times truncation [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(8105, 2097186, F8, 17) (dual of [2097186, 2097081, 18]-code), using
(88, 88+17, large)-Net in Base 8 — Upper bound on s
There is no (88, 105, large)-net in base 8, because
- 15 times m-reduction [i] would yield (88, 90, large)-net in base 8, but