Best Known (155−18, 155, s)-Nets in Base 8
(155−18, 155, 1864199)-Net over F8 — Constructive and digital
Digital (137, 155, 1864199)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 17, 65)-net over F8, using
- base reduction for projective spaces (embedding PG(8,64) in PG(16,8)) for nets [i] based on digital (0, 9, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- base reduction for projective spaces (embedding PG(8,64) in PG(16,8)) for nets [i] based on digital (0, 9, 65)-net over F64, using
- digital (120, 138, 1864134)-net over F8, using
- trace code for nets [i] based on digital (51, 69, 932067)-net over F64, using
- net defined by OOA [i] based on linear OOA(6469, 932067, F64, 18, 18) (dual of [(932067, 18), 16777137, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(6469, large, F64, 18) (dual of [large, large−69, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(6469, large, F64, 18) (dual of [large, large−69, 19]-code), using
- net defined by OOA [i] based on linear OOA(6469, 932067, F64, 18, 18) (dual of [(932067, 18), 16777137, 19]-NRT-code), using
- trace code for nets [i] based on digital (51, 69, 932067)-net over F64, using
- digital (8, 17, 65)-net over F8, using
(155−18, 155, large)-Net over F8 — Digital
Digital (137, 155, large)-net over F8, using
- 82 times duplication [i] based on digital (135, 153, large)-net over F8, using
- t-expansion [i] based on digital (131, 153, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8153, large, F8, 22) (dual of [large, large−153, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8153, large, F8, 22) (dual of [large, large−153, 23]-code), using
- t-expansion [i] based on digital (131, 153, large)-net over F8, using
(155−18, 155, large)-Net in Base 8 — Upper bound on s
There is no (137, 155, large)-net in base 8, because
- 16 times m-reduction [i] would yield (137, 139, large)-net in base 8, but