Best Known (70, 80, s)-Nets in Base 5
(70, 80, 1677720)-Net over F5 — Constructive and digital
Digital (70, 80, 1677720)-net over F5, using
- net defined by OOA [i] based on linear OOA(580, 1677720, F5, 10, 10) (dual of [(1677720, 10), 16777120, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(580, 8388600, F5, 10) (dual of [8388600, 8388520, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(580, large, F5, 10) (dual of [large, large−80, 11]-code), using
- the primitive narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(580, large, F5, 10) (dual of [large, large−80, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(580, 8388600, F5, 10) (dual of [8388600, 8388520, 11]-code), using
(70, 80, 7515512)-Net over F5 — Digital
Digital (70, 80, 7515512)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(580, 7515512, F5, 10) (dual of [7515512, 7515432, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(580, large, F5, 10) (dual of [large, large−80, 11]-code), using
- the primitive narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(580, large, F5, 10) (dual of [large, large−80, 11]-code), using
(70, 80, large)-Net in Base 5 — Upper bound on s
There is no (70, 80, large)-net in base 5, because
- 8 times m-reduction [i] would yield (70, 72, large)-net in base 5, but