Best Known (207, 241, s)-Nets in Base 3
(207, 241, 3483)-Net over F3 — Constructive and digital
Digital (207, 241, 3483)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (3, 20, 10)-net over F3, using
- net from sequence [i] based on digital (3, 9)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 3 and N(F) ≥ 10, using
- net from sequence [i] based on digital (3, 9)-sequence over F3, using
- digital (187, 221, 3473)-net over F3, using
- net defined by OOA [i] based on linear OOA(3221, 3473, F3, 34, 34) (dual of [(3473, 34), 117861, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(3221, 59041, F3, 34) (dual of [59041, 58820, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(3221, 59049, F3, 34) (dual of [59049, 58828, 35]-code), using
- an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- discarding factors / shortening the dual code based on linear OA(3221, 59049, F3, 34) (dual of [59049, 58828, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(3221, 59041, F3, 34) (dual of [59041, 58820, 35]-code), using
- net defined by OOA [i] based on linear OOA(3221, 3473, F3, 34, 34) (dual of [(3473, 34), 117861, 35]-NRT-code), using
- digital (3, 20, 10)-net over F3, using
(207, 241, 29559)-Net over F3 — Digital
Digital (207, 241, 29559)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3241, 29559, F3, 2, 34) (dual of [(29559, 2), 58877, 35]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3240, 29559, F3, 2, 34) (dual of [(29559, 2), 58878, 35]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3238, 29558, F3, 2, 34) (dual of [(29558, 2), 58878, 35]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3238, 59116, F3, 34) (dual of [59116, 58878, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(25) [i] based on
- linear OA(3221, 59049, F3, 34) (dual of [59049, 58828, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3171, 59049, F3, 26) (dual of [59049, 58878, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(317, 67, F3, 7) (dual of [67, 50, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(317, 80, F3, 7) (dual of [80, 63, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(317, 80, F3, 7) (dual of [80, 63, 8]-code), using
- construction X applied to Ce(33) ⊂ Ce(25) [i] based on
- OOA 2-folding [i] based on linear OA(3238, 59116, F3, 34) (dual of [59116, 58878, 35]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3238, 29558, F3, 2, 34) (dual of [(29558, 2), 58878, 35]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3240, 29559, F3, 2, 34) (dual of [(29559, 2), 58878, 35]-NRT-code), using
(207, 241, large)-Net in Base 3 — Upper bound on s
There is no (207, 241, large)-net in base 3, because
- 32 times m-reduction [i] would yield (207, 209, large)-net in base 3, but