Best Known (118−24, 118, s)-Nets in Base 16
(118−24, 118, 87384)-Net over F16 — Constructive and digital
Digital (94, 118, 87384)-net over F16, using
- net defined by OOA [i] based on linear OOA(16118, 87384, F16, 24, 24) (dual of [(87384, 24), 2097098, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(16118, 1048608, F16, 24) (dual of [1048608, 1048490, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(16118, 1048613, F16, 24) (dual of [1048613, 1048495, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- linear OA(16111, 1048576, F16, 24) (dual of [1048576, 1048465, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(1681, 1048576, F16, 18) (dual of [1048576, 1048495, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(167, 37, F16, 5) (dual of [37, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(167, 241, F16, 5) (dual of [241, 234, 6]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(16118, 1048613, F16, 24) (dual of [1048613, 1048495, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(16118, 1048608, F16, 24) (dual of [1048608, 1048490, 25]-code), using
(118−24, 118, 1048613)-Net over F16 — Digital
Digital (94, 118, 1048613)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16118, 1048613, F16, 24) (dual of [1048613, 1048495, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- linear OA(16111, 1048576, F16, 24) (dual of [1048576, 1048465, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(1681, 1048576, F16, 18) (dual of [1048576, 1048495, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(167, 37, F16, 5) (dual of [37, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(167, 241, F16, 5) (dual of [241, 234, 6]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
(118−24, 118, large)-Net in Base 16 — Upper bound on s
There is no (94, 118, large)-net in base 16, because
- 22 times m-reduction [i] would yield (94, 96, large)-net in base 16, but