Best Known (145−18, 145, s)-Nets in Base 5
(145−18, 145, 932067)-Net over F5 — Constructive and digital
Digital (127, 145, 932067)-net over F5, using
- 54 times duplication [i] based on digital (123, 141, 932067)-net over F5, using
- net defined by OOA [i] based on linear OOA(5141, 932067, F5, 18, 18) (dual of [(932067, 18), 16777065, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(5141, large, F5, 18) (dual of [large, large−141, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(5141, large, F5, 18) (dual of [large, large−141, 19]-code), using
- net defined by OOA [i] based on linear OOA(5141, 932067, F5, 18, 18) (dual of [(932067, 18), 16777065, 19]-NRT-code), using
(145−18, 145, 4194303)-Net over F5 — Digital
Digital (127, 145, 4194303)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(5145, 4194303, F5, 2, 18) (dual of [(4194303, 2), 8388461, 19]-NRT-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(5141, 4194301, F5, 2, 18) (dual of [(4194301, 2), 8388461, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5141, 8388602, F5, 18) (dual of [8388602, 8388461, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(5141, large, F5, 18) (dual of [large, large−141, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(5141, large, F5, 18) (dual of [large, large−141, 19]-code), using
- OOA 2-folding [i] based on linear OA(5141, 8388602, F5, 18) (dual of [8388602, 8388461, 19]-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(5141, 4194301, F5, 2, 18) (dual of [(4194301, 2), 8388461, 19]-NRT-code), using
(145−18, 145, large)-Net in Base 5 — Upper bound on s
There is no (127, 145, large)-net in base 5, because
- 16 times m-reduction [i] would yield (127, 129, large)-net in base 5, but