Best Known (115−14, 115, s)-Nets in Base 5
(115−14, 115, 1198371)-Net over F5 — Constructive and digital
Digital (101, 115, 1198371)-net over F5, using
- 54 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
(115−14, 115, 5774520)-Net over F5 — Digital
Digital (101, 115, 5774520)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5115, 5774520, F5, 14) (dual of [5774520, 5774405, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(5115, large, F5, 14) (dual of [large, large−115, 15]-code), using
- 4 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]
- 4 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(5115, large, F5, 14) (dual of [large, large−115, 15]-code), using
(115−14, 115, large)-Net in Base 5 — Upper bound on s
There is no (101, 115, large)-net in base 5, because
- 12 times m-reduction [i] would yield (101, 103, large)-net in base 5, but