Best Known (120−20, 120, s)-Nets in Base 8
(120−20, 120, 209715)-Net over F8 — Constructive and digital
Digital (100, 120, 209715)-net over F8, using
- net defined by OOA [i] based on linear OOA(8120, 209715, F8, 20, 20) (dual of [(209715, 20), 4194180, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(8120, 2097150, F8, 20) (dual of [2097150, 2097030, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(8120, 2097152, F8, 20) (dual of [2097152, 2097032, 21]-code), using
- an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(8120, 2097152, F8, 20) (dual of [2097152, 2097032, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(8120, 2097150, F8, 20) (dual of [2097150, 2097030, 21]-code), using
(120−20, 120, 1048579)-Net over F8 — Digital
Digital (100, 120, 1048579)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8120, 1048579, F8, 2, 20) (dual of [(1048579, 2), 2097038, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8120, 2097158, F8, 20) (dual of [2097158, 2097038, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(8120, 2097159, F8, 20) (dual of [2097159, 2097039, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(8120, 2097152, F8, 20) (dual of [2097152, 2097032, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(8113, 2097152, F8, 19) (dual of [2097152, 2097039, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(80, 7, F8, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(8120, 2097159, F8, 20) (dual of [2097159, 2097039, 21]-code), using
- OOA 2-folding [i] based on linear OA(8120, 2097158, F8, 20) (dual of [2097158, 2097038, 21]-code), using
(120−20, 120, large)-Net in Base 8 — Upper bound on s
There is no (100, 120, large)-net in base 8, because
- 18 times m-reduction [i] would yield (100, 102, large)-net in base 8, but