Best Known (125, 125+33, s)-Nets in Base 8
(125, 125+33, 2062)-Net over F8 — Constructive and digital
Digital (125, 158, 2062)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (1, 17, 14)-net over F8, using
- net from sequence [i] based on digital (1, 13)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 1 and N(F) ≥ 14, using
- net from sequence [i] based on digital (1, 13)-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 (1, 17, 14)-net over F8, using
(125, 125+33, 52592)-Net over F8 — Digital
Digital (125, 158, 52592)-net over F8, using
(125, 125+33, large)-Net in Base 8 — Upper bound on s
There is no (125, 158, large)-net in base 8, because
- 31 times m-reduction [i] would yield (125, 127, large)-net in base 8, but