Best Known (122, 122+14, s)-Nets in Base 5
(122, 122+14, 2396742)-Net over F5 — Constructive and digital
Digital (122, 136, 2396742)-net over F5, using
- 54 times duplication [i] based on digital (118, 132, 2396742)-net over F5, using
- trace code for nets [i] based on digital (52, 66, 1198371)-net over F25, using
- net defined by OOA [i] based on linear OOA(2566, 1198371, F25, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2566, 8388597, F25, 14) (dual of [8388597, 8388531, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2566, large, F25, 14) (dual of [large, large−66, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(2566, large, F25, 14) (dual of [large, large−66, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(2566, 8388597, F25, 14) (dual of [8388597, 8388531, 15]-code), using
- net defined by OOA [i] based on linear OOA(2566, 1198371, F25, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
- trace code for nets [i] based on digital (52, 66, 1198371)-net over F25, using
(122, 122+14, large)-Net over F5 — Digital
Digital (122, 136, large)-net over F5, using
- t-expansion [i] based on digital (121, 136, large)-net over F5, using
- 1 times m-reduction [i] based on digital (121, 137, large)-net over F5, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(5137, large, F5, 16) (dual of [large, large−137, 17]-code), using
- 16 times code embedding in larger space [i] based on linear OA(5121, large, F5, 16) (dual of [large, large−121, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 16 times code embedding in larger space [i] based on linear OA(5121, large, F5, 16) (dual of [large, large−121, 17]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(5137, large, F5, 16) (dual of [large, large−137, 17]-code), using
- 1 times m-reduction [i] based on digital (121, 137, large)-net over F5, using
(122, 122+14, large)-Net in Base 5 — Upper bound on s
There is no (122, 136, large)-net in base 5, because
- 12 times m-reduction [i] would yield (122, 124, large)-net in base 5, but