Best Known (135−15, 135, s)-Nets in Base 9
(135−15, 135, 2397142)-Net over F9 — Constructive and digital
Digital (120, 135, 2397142)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (14, 21, 400)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (2, 5, 212)-net over F9, using
- net defined by OOA [i] based on linear OOA(95, 212, F9, 3, 3) (dual of [(212, 3), 631, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(95, 212, F9, 2, 3) (dual of [(212, 2), 419, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(95, 212, F9, 3, 3) (dual of [(212, 3), 631, 4]-NRT-code), using
- digital (9, 16, 200)-net over F9, using
- trace code for nets [i] based on digital (1, 8, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- trace code for nets [i] based on digital (1, 8, 100)-net over F81, using
- digital (2, 5, 212)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (99, 114, 2396742)-net over F9, using
- trace code for nets [i] based on digital (42, 57, 1198371)-net over F81, using
- net defined by OOA [i] based on linear OOA(8157, 1198371, F81, 15, 15) (dual of [(1198371, 15), 17975508, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(8157, 8388598, F81, 15) (dual of [8388598, 8388541, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(8157, large, F81, 15) (dual of [large, large−57, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8157, large, F81, 15) (dual of [large, large−57, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(8157, 8388598, F81, 15) (dual of [8388598, 8388541, 16]-code), using
- net defined by OOA [i] based on linear OOA(8157, 1198371, F81, 15, 15) (dual of [(1198371, 15), 17975508, 16]-NRT-code), using
- trace code for nets [i] based on digital (42, 57, 1198371)-net over F81, using
- digital (14, 21, 400)-net over F9, using
(135−15, 135, large)-Net over F9 — Digital
Digital (120, 135, large)-net over F9, using
- t-expansion [i] based on digital (117, 135, large)-net over F9, using
- 2 times m-reduction [i] based on digital (117, 137, large)-net over F9, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(9137, large, F9, 20) (dual of [large, large−137, 21]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(9137, large, F9, 20) (dual of [large, large−137, 21]-code), using
- 2 times m-reduction [i] based on digital (117, 137, large)-net over F9, using
(135−15, 135, large)-Net in Base 9 — Upper bound on s
There is no (120, 135, large)-net in base 9, because
- 13 times m-reduction [i] would yield (120, 122, large)-net in base 9, but