Best Known (46−10, 46, s)-Nets in Base 16
(46−10, 46, 209716)-Net over F16 — Constructive and digital
Digital (36, 46, 209716)-net over F16, using
- net defined by OOA [i] based on linear OOA(1646, 209716, F16, 10, 10) (dual of [(209716, 10), 2097114, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(1646, 1048580, F16, 10) (dual of [1048580, 1048534, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(1646, 1048581, F16, 10) (dual of [1048581, 1048535, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(1646, 1048576, F16, 10) (dual of [1048576, 1048530, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1641, 1048576, F16, 9) (dual of [1048576, 1048535, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(160, 5, F16, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(1646, 1048581, F16, 10) (dual of [1048581, 1048535, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(1646, 1048580, F16, 10) (dual of [1048580, 1048534, 11]-code), using
(46−10, 46, 1048581)-Net over F16 — Digital
Digital (36, 46, 1048581)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1646, 1048581, F16, 10) (dual of [1048581, 1048535, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(1646, 1048576, F16, 10) (dual of [1048576, 1048530, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1641, 1048576, F16, 9) (dual of [1048576, 1048535, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(160, 5, F16, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
(46−10, 46, large)-Net in Base 16 — Upper bound on s
There is no (36, 46, large)-net in base 16, because
- 8 times m-reduction [i] would yield (36, 38, large)-net in base 16, but