Best Known (111, 111+16, s)-Nets in Base 8
(111, 111+16, 2097150)-Net over F8 — Constructive and digital
Digital (111, 127, 2097150)-net over F8, using
- 85 times duplication [i] based on 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
(111, 111+16, large)-Net over F8 — Digital
Digital (111, 127, large)-net over F8, using
- 83 times duplication [i] based on digital (108, 124, large)-net over F8, using
- t-expansion [i] based on digital (106, 124, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8124, large, F8, 18) (dual of [large, large−124, 19]-code), using
- 3 times code embedding in larger space [i] based on linear OA(8121, large, F8, 18) (dual of [large, large−121, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 3 times code embedding in larger space [i] based on linear OA(8121, large, F8, 18) (dual of [large, large−121, 19]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8124, large, F8, 18) (dual of [large, large−124, 19]-code), using
- t-expansion [i] based on digital (106, 124, large)-net over F8, using
(111, 111+16, large)-Net in Base 8 — Upper bound on s
There is no (111, 127, large)-net in base 8, because
- 14 times m-reduction [i] would yield (111, 113, large)-net in base 8, but