Best Known (165−33, 165, s)-Nets in Base 8
(165−33, 165, 2083)-Net over F8 — Constructive and digital
Digital (132, 165, 2083)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 24, 35)-net over F8, using
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 7, N(F) = 34, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using a function field by Sémirat [i]
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- digital (108, 141, 2048)-net over F8, using
- net defined by OOA [i] based on linear OOA(8141, 2048, F8, 33, 33) (dual of [(2048, 33), 67443, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [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]
- OOA 16-folding and stacking with additional row [i] based on linear OA(8141, 32769, F8, 33) (dual of [32769, 32628, 34]-code), using
- net defined by OOA [i] based on linear OOA(8141, 2048, F8, 33, 33) (dual of [(2048, 33), 67443, 34]-NRT-code), using
- digital (8, 24, 35)-net over F8, using
(165−33, 165, 4096)-Net in Base 8 — Constructive
(132, 165, 4096)-net in base 8, using
- 81 times duplication [i] based on (131, 164, 4096)-net in base 8, using
- base change [i] based on digital (90, 123, 4096)-net over F16, using
- 162 times duplication [i] based on digital (88, 121, 4096)-net over F16, using
- net defined by OOA [i] based on linear OOA(16121, 4096, F16, 33, 33) (dual of [(4096, 33), 135047, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [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]
- OOA 16-folding and stacking with additional row [i] based on linear OA(16121, 65537, F16, 33) (dual of [65537, 65416, 34]-code), using
- net defined by OOA [i] based on linear OOA(16121, 4096, F16, 33, 33) (dual of [(4096, 33), 135047, 34]-NRT-code), using
- 162 times duplication [i] based on digital (88, 121, 4096)-net over F16, using
- base change [i] based on digital (90, 123, 4096)-net over F16, using
(165−33, 165, 82875)-Net over F8 — Digital
Digital (132, 165, 82875)-net over F8, using
(165−33, 165, large)-Net in Base 8 — Upper bound on s
There is no (132, 165, large)-net in base 8, because
- 31 times m-reduction [i] would yield (132, 134, large)-net in base 8, but