Best Known (108, 140, s)-Nets in Base 8
(108, 140, 2048)-Net over F8 — Constructive and digital
Digital (108, 140, 2048)-net over F8, using
- net defined by OOA [i] based on linear OOA(8140, 2048, F8, 32, 32) (dual of [(2048, 32), 65396, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(8140, 32768, F8, 32) (dual of [32768, 32628, 33]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(8141, 32769, F8, 33) (dual of [32769, 32628, 34]-code), using
- OA 16-folding and stacking [i] based on linear OA(8140, 32768, F8, 32) (dual of [32768, 32628, 33]-code), using
(108, 140, 26285)-Net over F8 — Digital
Digital (108, 140, 26285)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8140, 26285, F8, 32) (dual of [26285, 26145, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(8140, 32768, F8, 32) (dual of [32768, 32628, 33]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(8141, 32769, F8, 33) (dual of [32769, 32628, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(8140, 32768, F8, 32) (dual of [32768, 32628, 33]-code), using
(108, 140, large)-Net in Base 8 — Upper bound on s
There is no (108, 140, large)-net in base 8, because
- 30 times m-reduction [i] would yield (108, 110, large)-net in base 8, but