Best Known (128, 128+17, s)-Nets in Base 5
(128, 128+17, 1048596)-Net over F5 — Constructive and digital
Digital (128, 145, 1048596)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (6, 14, 21)-net over F5, using
- net from sequence [i] based on digital (6, 20)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 6 and N(F) ≥ 21, using
- net from sequence [i] based on digital (6, 20)-sequence over F5, using
- digital (114, 131, 1048575)-net over F5, using
- net defined by OOA [i] based on linear OOA(5131, 1048575, F5, 17, 17) (dual of [(1048575, 17), 17825644, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(5131, 8388601, F5, 17) (dual of [8388601, 8388470, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(5131, large, F5, 17) (dual of [large, large−131, 18]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(5131, large, F5, 17) (dual of [large, large−131, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(5131, 8388601, F5, 17) (dual of [8388601, 8388470, 18]-code), using
- net defined by OOA [i] based on linear OOA(5131, 1048575, F5, 17, 17) (dual of [(1048575, 17), 17825644, 18]-NRT-code), using
- digital (6, 14, 21)-net over F5, using
(128, 128+17, 8237931)-Net over F5 — Digital
Digital (128, 145, 8237931)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5145, 8237931, F5, 17) (dual of [8237931, 8237786, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(5145, large, F5, 17) (dual of [large, large−145, 18]-code), using
- 14 times code embedding in larger space [i] based on linear OA(5131, large, F5, 17) (dual of [large, large−131, 18]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- 14 times code embedding in larger space [i] based on linear OA(5131, large, F5, 17) (dual of [large, large−131, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(5145, large, F5, 17) (dual of [large, large−145, 18]-code), using
(128, 128+17, large)-Net in Base 5 — Upper bound on s
There is no (128, 145, large)-net in base 5, because
- 15 times m-reduction [i] would yield (128, 130, large)-net in base 5, but