Best Known (110, 110+16, s)-Nets in Base 5
(110, 110+16, 1048575)-Net over F5 — Constructive and digital
Digital (110, 126, 1048575)-net over F5, using
- 55 times duplication [i] based on digital (105, 121, 1048575)-net over F5, using
- net defined by OOA [i] based on linear OOA(5121, 1048575, F5, 16, 16) (dual of [(1048575, 16), 16777079, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(5121, 8388600, F5, 16) (dual of [8388600, 8388479, 17]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(5121, large, F5, 16) (dual of [large, large−121, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(5121, 8388600, F5, 16) (dual of [8388600, 8388479, 17]-code), using
- net defined by OOA [i] based on linear OOA(5121, 1048575, F5, 16, 16) (dual of [(1048575, 16), 16777079, 17]-NRT-code), using
(110, 110+16, 4194303)-Net over F5 — Digital
Digital (110, 126, 4194303)-net over F5, using
- 51 times duplication [i] based on digital (109, 125, 4194303)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(5125, 4194303, F5, 2, 16) (dual of [(4194303, 2), 8388481, 17]-NRT-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(5121, 4194301, F5, 2, 16) (dual of [(4194301, 2), 8388481, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5121, 8388602, F5, 16) (dual of [8388602, 8388481, 17]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(5121, large, F5, 16) (dual of [large, large−121, 17]-code), using
- OOA 2-folding [i] based on linear OA(5121, 8388602, F5, 16) (dual of [8388602, 8388481, 17]-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(5121, 4194301, F5, 2, 16) (dual of [(4194301, 2), 8388481, 17]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(5125, 4194303, F5, 2, 16) (dual of [(4194303, 2), 8388481, 17]-NRT-code), using
(110, 110+16, large)-Net in Base 5 — Upper bound on s
There is no (110, 126, large)-net in base 5, because
- 14 times m-reduction [i] would yield (110, 112, large)-net in base 5, but