Best Known (107, 121, s)-Nets in Base 5
(107, 121, 1198396)-Net over F5 — Constructive and digital
Digital (107, 121, 1198396)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (3, 10, 25)-net over F5, using
- 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
(107, 121, large)-Net over F5 — Digital
Digital (107, 121, large)-net over F5, using
- 53 times duplication [i] based on digital (104, 118, large)-net over F5, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(5118, large, F5, 14) (dual of [large, large−118, 15]-code), using
- 7 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]
- 7 times code embedding in larger space [i] based on linear OA(5111, large, F5, 14) (dual of [large, large−111, 15]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(5118, large, F5, 14) (dual of [large, large−118, 15]-code), using
(107, 121, large)-Net in Base 5 — Upper bound on s
There is no (107, 121, large)-net in base 5, because
- 12 times m-reduction [i] would yield (107, 109, large)-net in base 5, but