Best Known (100, 100+25, s)-Nets in Base 16
(100, 100+25, 87384)-Net over F16 — Constructive and digital
Digital (100, 125, 87384)-net over F16, using
- 162 times duplication [i] based on digital (98, 123, 87384)-net over F16, using
- net defined by OOA [i] based on linear OOA(16123, 87384, F16, 25, 25) (dual of [(87384, 25), 2184477, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(16123, 1048609, F16, 25) (dual of [1048609, 1048486, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(16123, 1048613, F16, 25) (dual of [1048613, 1048490, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(18) [i] based on
- linear OA(16116, 1048576, F16, 25) (dual of [1048576, 1048460, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(1686, 1048576, F16, 19) (dual of [1048576, 1048490, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(24) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(16123, 1048613, F16, 25) (dual of [1048613, 1048490, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(16123, 1048609, F16, 25) (dual of [1048609, 1048486, 26]-code), using
- net defined by OOA [i] based on linear OOA(16123, 87384, F16, 25, 25) (dual of [(87384, 25), 2184477, 26]-NRT-code), using
(100, 100+25, 1221051)-Net over F16 — Digital
Digital (100, 125, 1221051)-net over F16, using
(100, 100+25, large)-Net in Base 16 — Upper bound on s
There is no (100, 125, large)-net in base 16, because
- 23 times m-reduction [i] would yield (100, 102, large)-net in base 16, but