Best Known (104, 119, s)-Nets in Base 16
(104, 119, 2746272)-Net over F16 — Constructive and digital
Digital (104, 119, 2746272)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (26, 33, 349530)-net over F16, using
- net defined by OOA [i] based on linear OOA(1633, 349530, F16, 7, 7) (dual of [(349530, 7), 2446677, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(1633, 1048591, F16, 7) (dual of [1048591, 1048558, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(1633, 1048593, F16, 7) (dual of [1048593, 1048560, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(3) [i] based on
- linear OA(1631, 1048576, F16, 7) (dual of [1048576, 1048545, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(1616, 1048576, F16, 4) (dual of [1048576, 1048560, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(6) ⊂ Ce(3) [i] based on
- discarding factors / shortening the dual code based on linear OA(1633, 1048593, F16, 7) (dual of [1048593, 1048560, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(1633, 1048591, F16, 7) (dual of [1048591, 1048558, 8]-code), using
- net defined by OOA [i] based on linear OOA(1633, 349530, F16, 7, 7) (dual of [(349530, 7), 2446677, 8]-NRT-code), using
- digital (71, 86, 2396742)-net over F16, using
- trace code for nets [i] based on digital (28, 43, 1198371)-net over F256, using
- net defined by OOA [i] based on linear OOA(25643, 1198371, F256, 15, 15) (dual of [(1198371, 15), 17975522, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25643, 8388598, F256, 15) (dual of [8388598, 8388555, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25643, 8388598, F256, 15) (dual of [8388598, 8388555, 16]-code), using
- net defined by OOA [i] based on linear OOA(25643, 1198371, F256, 15, 15) (dual of [(1198371, 15), 17975522, 16]-NRT-code), using
- trace code for nets [i] based on digital (28, 43, 1198371)-net over F256, using
- digital (26, 33, 349530)-net over F16, using
(104, 119, large)-Net over F16 — Digital
Digital (104, 119, large)-net over F16, using
- 8 times m-reduction [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
(104, 119, large)-Net in Base 16 — Upper bound on s
There is no (104, 119, large)-net in base 16, because
- 13 times m-reduction [i] would yield (104, 106, large)-net in base 16, but