Best Known (17, 35, s)-Nets in Base 128
(17, 35, 1820)-Net over F128 — Constructive and digital
Digital (17, 35, 1820)-net over F128, using
- net defined by OOA [i] based on linear OOA(12835, 1820, F128, 18, 18) (dual of [(1820, 18), 32725, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(12835, 16380, F128, 18) (dual of [16380, 16345, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using
- an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(12835, 16380, F128, 18) (dual of [16380, 16345, 19]-code), using
(17, 35, 4096)-Net over F128 — Digital
Digital (17, 35, 4096)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12835, 4096, F128, 4, 18) (dual of [(4096, 4), 16349, 19]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using
- an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- OOA 4-folding [i] based on linear OA(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using
(17, 35, 5112729)-Net in Base 128 — Upper bound on s
There is no (17, 35, 5112730)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 56 539152 532055 963109 800890 688331 342055 671412 523625 516862 409044 686829 377873 > 12835 [i]