Best Known (112, 112+33, s)-Nets in Base 8
(112, 112+33, 2049)-Net over F8 — Constructive and digital
Digital (112, 145, 2049)-net over F8, using
- net defined by OOA [i] based on linear OOA(8145, 2049, F8, 33, 33) (dual of [(2049, 33), 67472, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(8145, 32785, F8, 33) (dual of [32785, 32640, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(8145, 32787, F8, 33) (dual of [32787, 32642, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(28) [i] based on
- linear OA(8141, 32768, F8, 33) (dual of [32768, 32627, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(8126, 32768, F8, 29) (dual of [32768, 32642, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(84, 19, F8, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,8)), using
- construction X applied to Ce(32) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(8145, 32787, F8, 33) (dual of [32787, 32642, 34]-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(8145, 32785, F8, 33) (dual of [32785, 32640, 34]-code), using
(112, 112+33, 27774)-Net over F8 — Digital
Digital (112, 145, 27774)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8145, 27774, F8, 33) (dual of [27774, 27629, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(8145, 32783, F8, 33) (dual of [32783, 32638, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [i] based on
- linear OA(8141, 32769, F8, 33) (dual of [32769, 32628, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(8131, 32769, F8, 29) (dual of [32769, 32638, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(84, 14, F8, 3) (dual of [14, 10, 4]-code or 14-cap in PG(3,8)), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [i] based on
- discarding factors / shortening the dual code based on linear OA(8145, 32783, F8, 33) (dual of [32783, 32638, 34]-code), using
(112, 112+33, large)-Net in Base 8 — Upper bound on s
There is no (112, 145, large)-net in base 8, because
- 31 times m-reduction [i] would yield (112, 114, large)-net in base 8, but