Best Known (135−22, 135, s)-Nets in Base 8
(135−22, 135, 190651)-Net over F8 — Constructive and digital
Digital (113, 135, 190651)-net over F8, using
- net defined by OOA [i] based on linear OOA(8135, 190651, F8, 22, 22) (dual of [(190651, 22), 4194187, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(8135, 2097161, F8, 22) (dual of [2097161, 2097026, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(8135, 2097167, F8, 22) (dual of [2097167, 2097032, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(8134, 2097152, F8, 22) (dual of [2097152, 2097018, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 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(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(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(8135, 2097167, F8, 22) (dual of [2097167, 2097032, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(8135, 2097161, F8, 22) (dual of [2097161, 2097026, 23]-code), using
(135−22, 135, 1333237)-Net over F8 — Digital
Digital (113, 135, 1333237)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8135, 1333237, F8, 22) (dual of [1333237, 1333102, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(8135, 2097167, F8, 22) (dual of [2097167, 2097032, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(8134, 2097152, F8, 22) (dual of [2097152, 2097018, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 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(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(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(8135, 2097167, F8, 22) (dual of [2097167, 2097032, 23]-code), using
(135−22, 135, large)-Net in Base 8 — Upper bound on s
There is no (113, 135, large)-net in base 8, because
- 20 times m-reduction [i] would yield (113, 115, large)-net in base 8, but