Best Known (141, 157, s)-Nets in Base 8
(141, 157, 2105341)-Net over F8 — Constructive and digital
Digital (141, 157, 2105341)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (27, 35, 8191)-net over F8, using
- net defined by OOA [i] based on linear OOA(835, 8191, F8, 8, 8) (dual of [(8191, 8), 65493, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(835, 32764, F8, 8) (dual of [32764, 32729, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(835, 32767, F8, 8) (dual of [32767, 32732, 9]-code), using
- 1 times truncation [i] based on linear OA(836, 32768, F8, 9) (dual of [32768, 32732, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- 1 times truncation [i] based on linear OA(836, 32768, F8, 9) (dual of [32768, 32732, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(835, 32767, F8, 8) (dual of [32767, 32732, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(835, 32764, F8, 8) (dual of [32764, 32729, 9]-code), using
- net defined by OOA [i] based on linear OOA(835, 8191, F8, 8, 8) (dual of [(8191, 8), 65493, 9]-NRT-code), using
- digital (106, 122, 2097150)-net over F8, using
- net defined by OOA [i] based on linear OOA(8122, 2097150, F8, 18, 16) (dual of [(2097150, 18), 37748578, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(8122, 8388601, F8, 2, 16) (dual of [(8388601, 2), 16777080, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8122, 8388602, F8, 2, 16) (dual of [(8388602, 2), 16777082, 17]-NRT-code), using
- trace code [i] based on linear OOA(6461, 4194301, F64, 2, 16) (dual of [(4194301, 2), 8388541, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6461, 8388602, F64, 16) (dual of [8388602, 8388541, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(6461, large, F64, 16) (dual of [large, large−61, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(6461, large, F64, 16) (dual of [large, large−61, 17]-code), using
- OOA 2-folding [i] based on linear OA(6461, 8388602, F64, 16) (dual of [8388602, 8388541, 17]-code), using
- trace code [i] based on linear OOA(6461, 4194301, F64, 2, 16) (dual of [(4194301, 2), 8388541, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8122, 8388602, F8, 2, 16) (dual of [(8388602, 2), 16777082, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(8122, 8388601, F8, 2, 16) (dual of [(8388601, 2), 16777080, 17]-NRT-code), using
- net defined by OOA [i] based on linear OOA(8122, 2097150, F8, 18, 16) (dual of [(2097150, 18), 37748578, 17]-NRT-code), using
- digital (27, 35, 8191)-net over F8, using
(141, 157, large)-Net over F8 — Digital
Digital (141, 157, large)-net over F8, using
- t-expansion [i] based on digital (138, 157, large)-net over F8, using
- 4 times m-reduction [i] based on digital (138, 161, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8161, large, F8, 23) (dual of [large, large−161, 24]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 816−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8161, large, F8, 23) (dual of [large, large−161, 24]-code), using
- 4 times m-reduction [i] based on digital (138, 161, large)-net over F8, using
(141, 157, large)-Net in Base 8 — Upper bound on s
There is no (141, 157, large)-net in base 8, because
- 14 times m-reduction [i] would yield (141, 143, large)-net in base 8, but