Best Known (99−12, 99, s)-Nets in Base 5
(99−12, 99, 1398114)-Net over F5 — Constructive and digital
Digital (87, 99, 1398114)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (2, 8, 14)-net over F5, using
- digital (79, 91, 1398100)-net over F5, using
- net defined by OOA [i] based on linear OOA(591, 1398100, F5, 12, 12) (dual of [(1398100, 12), 16777109, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(591, 8388600, F5, 12) (dual of [8388600, 8388509, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(591, large, F5, 12) (dual of [large, large−91, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(591, large, F5, 12) (dual of [large, large−91, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(591, 8388600, F5, 12) (dual of [8388600, 8388509, 13]-code), using
- net defined by OOA [i] based on linear OOA(591, 1398100, F5, 12, 12) (dual of [(1398100, 12), 16777109, 13]-NRT-code), using
(99−12, 99, 8013496)-Net over F5 — Digital
Digital (87, 99, 8013496)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(599, 8013496, F5, 12) (dual of [8013496, 8013397, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(599, large, F5, 12) (dual of [large, large−99, 13]-code), using
- 8 times code embedding in larger space [i] based on linear OA(591, large, F5, 12) (dual of [large, large−91, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- 8 times code embedding in larger space [i] based on linear OA(591, large, F5, 12) (dual of [large, large−91, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(599, large, F5, 12) (dual of [large, large−99, 13]-code), using
(99−12, 99, large)-Net in Base 5 — Upper bound on s
There is no (87, 99, large)-net in base 5, because
- 10 times m-reduction [i] would yield (87, 89, large)-net in base 5, but