Best Known (98, 98+26, s)-Nets in Base 16
(98, 98+26, 80661)-Net over F16 — Constructive and digital
Digital (98, 124, 80661)-net over F16, using
- 161 times duplication [i] based on digital (97, 123, 80661)-net over F16, using
- net defined by OOA [i] based on linear OOA(16123, 80661, F16, 26, 26) (dual of [(80661, 26), 2097063, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(16123, 1048593, F16, 26) (dual of [1048593, 1048470, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- linear OA(16121, 1048576, F16, 26) (dual of [1048576, 1048455, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(16106, 1048576, F16, 23) (dual of [1048576, 1048470, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(25) ⊂ Ce(22) [i] based on
- OA 13-folding and stacking [i] based on linear OA(16123, 1048593, F16, 26) (dual of [1048593, 1048470, 27]-code), using
- net defined by OOA [i] based on linear OOA(16123, 80661, F16, 26, 26) (dual of [(80661, 26), 2097063, 27]-NRT-code), using
(98, 98+26, 969127)-Net over F16 — Digital
Digital (98, 124, 969127)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16124, 969127, F16, 26) (dual of [969127, 969003, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(16124, 1048594, F16, 26) (dual of [1048594, 1048470, 27]-code), using
- 1 times code embedding in larger space [i] based on linear OA(16123, 1048593, F16, 26) (dual of [1048593, 1048470, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- linear OA(16121, 1048576, F16, 26) (dual of [1048576, 1048455, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(16106, 1048576, F16, 23) (dual of [1048576, 1048470, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(25) ⊂ Ce(22) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(16123, 1048593, F16, 26) (dual of [1048593, 1048470, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(16124, 1048594, F16, 26) (dual of [1048594, 1048470, 27]-code), using
(98, 98+26, large)-Net in Base 16 — Upper bound on s
There is no (98, 124, large)-net in base 16, because
- 24 times m-reduction [i] would yield (98, 100, large)-net in base 16, but