Best Known (45−6, 45, s)-Nets in Base 8
(45−6, 45, 5592411)-Net over F8 — Constructive and digital
Digital (39, 45, 5592411)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 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]
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- digital (36, 42, 5592402)-net over F8, using
- trace code for nets [i] based on digital (15, 21, 2796201)-net over F64, using
- net defined by OOA [i] based on linear OOA(6421, 2796201, F64, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(6421, large, F64, 6) (dual of [large, large−21, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(6421, large, F64, 6) (dual of [large, large−21, 7]-code), using
- net defined by OOA [i] based on linear OOA(6421, 2796201, F64, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
- trace code for nets [i] based on digital (15, 21, 2796201)-net over F64, using
- digital (0, 3, 9)-net over F8, using
(45−6, 45, large)-Net over F8 — Digital
Digital (39, 45, large)-net over F8, using
- 84 times duplication [i] based on digital (35, 41, large)-net over F8, using
(45−6, 45, large)-Net in Base 8 — Upper bound on s
There is no (39, 45, large)-net in base 8, because
- 4 times m-reduction [i] would yield (39, 41, large)-net in base 8, but