Best Known (114, 130, s)-Nets in Base 16
(114, 130, 2359298)-Net over F16 — Constructive and digital
Digital (114, 130, 2359298)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (30, 38, 262148)-net over F16, using
- net defined by OOA [i] based on linear OOA(1638, 262148, F16, 8, 8) (dual of [(262148, 8), 2097146, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(1638, 1048592, F16, 8) (dual of [1048592, 1048554, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(1638, 1048593, F16, 8) (dual of [1048593, 1048555, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(4) [i] based on
- linear OA(1636, 1048576, F16, 8) (dual of [1048576, 1048540, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(1621, 1048576, F16, 5) (dual of [1048576, 1048555, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(162, 17, F16, 2) (dual of [17, 15, 3]-code or 17-arc in PG(1,16)), using
- extended Reed–Solomon code RSe(15,16) [i]
- Hamming code H(2,16) [i]
- construction X applied to Ce(7) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(1638, 1048593, F16, 8) (dual of [1048593, 1048555, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(1638, 1048592, F16, 8) (dual of [1048592, 1048554, 9]-code), using
- net defined by OOA [i] based on linear OOA(1638, 262148, F16, 8, 8) (dual of [(262148, 8), 2097146, 9]-NRT-code), using
- digital (76, 92, 2097150)-net over F16, using
- net defined by OOA [i] based on linear OOA(1692, 2097150, F16, 18, 16) (dual of [(2097150, 18), 37748608, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(1692, 8388601, F16, 2, 16) (dual of [(8388601, 2), 16777110, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1692, 8388602, F16, 2, 16) (dual of [(8388602, 2), 16777112, 17]-NRT-code), using
- trace code [i] based on linear OOA(25646, 4194301, F256, 2, 16) (dual of [(4194301, 2), 8388556, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25646, 8388602, F256, 16) (dual of [8388602, 8388556, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(25646, large, F256, 16) (dual of [large, large−46, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(25646, large, F256, 16) (dual of [large, large−46, 17]-code), using
- OOA 2-folding [i] based on linear OA(25646, 8388602, F256, 16) (dual of [8388602, 8388556, 17]-code), using
- trace code [i] based on linear OOA(25646, 4194301, F256, 2, 16) (dual of [(4194301, 2), 8388556, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1692, 8388602, F16, 2, 16) (dual of [(8388602, 2), 16777112, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(1692, 8388601, F16, 2, 16) (dual of [(8388601, 2), 16777110, 17]-NRT-code), using
- net defined by OOA [i] based on linear OOA(1692, 2097150, F16, 18, 16) (dual of [(2097150, 18), 37748608, 17]-NRT-code), using
- digital (30, 38, 262148)-net over F16, using
(114, 130, large)-Net over F16 — Digital
Digital (114, 130, large)-net over F16, using
- 163 times duplication [i] based on digital (111, 127, large)-net over F16, using
- t-expansion [i] based on digital (104, 127, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16127, large, F16, 23) (dual of [large, large−127, 24]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16127, large, F16, 23) (dual of [large, large−127, 24]-code), using
- t-expansion [i] based on digital (104, 127, large)-net over F16, using
(114, 130, large)-Net in Base 16 — Upper bound on s
There is no (114, 130, large)-net in base 16, because
- 14 times m-reduction [i] would yield (114, 116, large)-net in base 16, but