Best Known (130−18, 130, s)-Nets in Base 8
(130−18, 130, 932076)-Net over F8 — Constructive and digital
Digital (112, 130, 932076)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 9)-net over F8, using
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 0 and N(F) ≥ 9, using
- the rational function field F8(x) [i]
- Niederreiter sequence [i]
- a shift-net [i]
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- digital (103, 121, 932067)-net over F8, using
- net defined by OOA [i] based on linear OOA(8121, 932067, F8, 18, 18) (dual of [(932067, 18), 16777085, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(8121, large, F8, 18) (dual of [large, large−121, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(8121, large, F8, 18) (dual of [large, large−121, 19]-code), using
- net defined by OOA [i] based on linear OOA(8121, 932067, F8, 18, 18) (dual of [(932067, 18), 16777085, 19]-NRT-code), using
- digital (0, 9, 9)-net over F8, using
(130−18, 130, large)-Net over F8 — Digital
Digital (112, 130, large)-net over F8, using
- 86 times duplication [i] based on digital (106, 124, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8124, large, F8, 18) (dual of [large, large−124, 19]-code), using
- 3 times code embedding in larger space [i] based on linear OA(8121, large, F8, 18) (dual of [large, large−121, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 3 times code embedding in larger space [i] based on linear OA(8121, large, F8, 18) (dual of [large, large−121, 19]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8124, large, F8, 18) (dual of [large, large−124, 19]-code), using
(130−18, 130, large)-Net in Base 8 — Upper bound on s
There is no (112, 130, large)-net in base 8, because
- 16 times m-reduction [i] would yield (112, 114, large)-net in base 8, but