Best Known (121−20, 121, s)-Nets in Base 8
(121−20, 121, 209716)-Net over F8 — Constructive and digital
Digital (101, 121, 209716)-net over F8, using
- net defined by OOA [i] based on linear OOA(8121, 209716, F8, 20, 20) (dual of [(209716, 20), 4194199, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(8121, 2097160, F8, 20) (dual of [2097160, 2097039, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(8121, 2097167, F8, 20) (dual of [2097167, 2097046, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(17) [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(8106, 2097152, F8, 18) (dual of [2097152, 2097046, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(81, 15, F8, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(8121, 2097167, F8, 20) (dual of [2097167, 2097046, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(8121, 2097160, F8, 20) (dual of [2097160, 2097039, 21]-code), using
(121−20, 121, 1131430)-Net over F8 — Digital
Digital (101, 121, 1131430)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8121, 1131430, F8, 20) (dual of [1131430, 1131309, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(8121, 2097167, F8, 20) (dual of [2097167, 2097046, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(17) [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(8106, 2097152, F8, 18) (dual of [2097152, 2097046, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(81, 15, F8, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(8121, 2097167, F8, 20) (dual of [2097167, 2097046, 21]-code), using
(121−20, 121, large)-Net in Base 8 — Upper bound on s
There is no (101, 121, large)-net in base 8, because
- 18 times m-reduction [i] would yield (101, 103, large)-net in base 8, but