Best Known (100, 100+20, s)-Nets in Base 5
(100, 100+20, 7816)-Net over F5 — Constructive and digital
Digital (100, 120, 7816)-net over F5, using
- net defined by OOA [i] based on linear OOA(5120, 7816, F5, 20, 20) (dual of [(7816, 20), 156200, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(5120, 78160, F5, 20) (dual of [78160, 78040, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(5120, 78161, F5, 20) (dual of [78161, 78041, 21]-code), using
- construction X applied to C([0,10]) ⊂ C([0,7]) [i] based on
- linear OA(5113, 78126, F5, 21) (dual of [78126, 78013, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(585, 78126, F5, 15) (dual of [78126, 78041, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(57, 35, F5, 4) (dual of [35, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 44, F5, 4) (dual of [44, 37, 5]-code), using
- construction X applied to C([0,10]) ⊂ C([0,7]) [i] based on
- discarding factors / shortening the dual code based on linear OA(5120, 78161, F5, 20) (dual of [78161, 78041, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(5120, 78160, F5, 20) (dual of [78160, 78040, 21]-code), using
(100, 100+20, 78161)-Net over F5 — Digital
Digital (100, 120, 78161)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5120, 78161, F5, 20) (dual of [78161, 78041, 21]-code), using
- construction X applied to C([0,10]) ⊂ C([0,7]) [i] based on
- linear OA(5113, 78126, F5, 21) (dual of [78126, 78013, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(585, 78126, F5, 15) (dual of [78126, 78041, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(57, 35, F5, 4) (dual of [35, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 44, F5, 4) (dual of [44, 37, 5]-code), using
- construction X applied to C([0,10]) ⊂ C([0,7]) [i] based on
(100, 100+20, large)-Net in Base 5 — Upper bound on s
There is no (100, 120, large)-net in base 5, because
- 18 times m-reduction [i] would yield (100, 102, large)-net in base 5, but