Best Known (113−14, 113, s)-Nets in Base 5
(113−14, 113, 1198371)-Net over F5 — Constructive and digital
Digital (99, 113, 1198371)-net over F5, using
- 52 times duplication [i] based on digital (97, 111, 1198371)-net over F5, using
- net defined by OOA [i] based on linear OOA(5111, 1198371, F5, 14, 14) (dual of [(1198371, 14), 16777083, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(5111, 8388597, F5, 14) (dual of [8388597, 8388486, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(5111, large, F5, 14) (dual of [large, large−111, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(5111, large, F5, 14) (dual of [large, large−111, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(5111, 8388597, F5, 14) (dual of [8388597, 8388486, 15]-code), using
- net defined by OOA [i] based on linear OOA(5111, 1198371, F5, 14, 14) (dual of [(1198371, 14), 16777083, 15]-NRT-code), using
(113−14, 113, 4415915)-Net over F5 — Digital
Digital (99, 113, 4415915)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5113, 4415915, F5, 14) (dual of [4415915, 4415802, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(5113, large, F5, 14) (dual of [large, large−113, 15]-code), using
- 2 times code embedding in larger space [i] based on linear OA(5111, large, F5, 14) (dual of [large, large−111, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 2 times code embedding in larger space [i] based on linear OA(5111, large, F5, 14) (dual of [large, large−111, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(5113, large, F5, 14) (dual of [large, large−113, 15]-code), using
(113−14, 113, large)-Net in Base 5 — Upper bound on s
There is no (99, 113, large)-net in base 5, because
- 12 times m-reduction [i] would yield (99, 101, large)-net in base 5, but