Best Known (129, 129+32, s)-Nets in Base 8
(129, 129+32, 2076)-Net over F8 — Constructive and digital
Digital (129, 161, 2076)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 21, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- 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
- net defined by OOA [i] based on linear OOA(8140, 2048, F8, 32, 32) (dual of [(2048, 32), 65396, 33]-NRT-code), using
- digital (5, 21, 28)-net over F8, using
(129, 129+32, 4096)-Net in Base 8 — Constructive
(129, 161, 4096)-net in base 8, using
- 1 times m-reduction [i] based on (129, 162, 4096)-net in base 8, using
- net defined by OOA [i] based on OOA(8162, 4096, S8, 33, 33), using
- OOA 16-folding and stacking with additional row [i] based on OA(8162, 65537, S8, 33), using
- discarding parts of the base [i] based on linear OA(16121, 65537, F16, 33) (dual of [65537, 65416, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 168−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- discarding parts of the base [i] based on linear OA(16121, 65537, F16, 33) (dual of [65537, 65416, 34]-code), using
- OOA 16-folding and stacking with additional row [i] based on OA(8162, 65537, S8, 33), using
- net defined by OOA [i] based on OOA(8162, 4096, S8, 33, 33), using
(129, 129+32, 86947)-Net over F8 — Digital
Digital (129, 161, 86947)-net over F8, using
(129, 129+32, large)-Net in Base 8 — Upper bound on s
There is no (129, 161, large)-net in base 8, because
- 30 times m-reduction [i] would yield (129, 131, large)-net in base 8, but