Best Known (156−36, 156, s)-Nets in Base 8
(156−36, 156, 1820)-Net over F8 — Constructive and digital
Digital (120, 156, 1820)-net over F8, using
- net defined by OOA [i] based on linear OOA(8156, 1820, F8, 36, 36) (dual of [(1820, 36), 65364, 37]-NRT-code), using
- OA 18-folding and stacking [i] based on linear OA(8156, 32760, F8, 36) (dual of [32760, 32604, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(8156, 32768, F8, 36) (dual of [32768, 32612, 37]-code), using
- an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- discarding factors / shortening the dual code based on linear OA(8156, 32768, F8, 36) (dual of [32768, 32612, 37]-code), using
- OA 18-folding and stacking [i] based on linear OA(8156, 32760, F8, 36) (dual of [32760, 32604, 37]-code), using
(156−36, 156, 25296)-Net over F8 — Digital
Digital (120, 156, 25296)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8156, 25296, F8, 36) (dual of [25296, 25140, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(8156, 32768, F8, 36) (dual of [32768, 32612, 37]-code), using
- an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- discarding factors / shortening the dual code based on linear OA(8156, 32768, F8, 36) (dual of [32768, 32612, 37]-code), using
(156−36, 156, large)-Net in Base 8 — Upper bound on s
There is no (120, 156, large)-net in base 8, because
- 34 times m-reduction [i] would yield (120, 122, large)-net in base 8, but