Best Known (206, 243, s)-Nets in Base 3
(206, 243, 3281)-Net over F3 — Constructive and digital
Digital (206, 243, 3281)-net over F3, using
- 31 times duplication [i] based on digital (205, 242, 3281)-net over F3, using
- net defined by OOA [i] based on linear OOA(3242, 3281, F3, 37, 37) (dual of [(3281, 37), 121155, 38]-NRT-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(3242, 59059, F3, 37) (dual of [59059, 58817, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(3242, 59060, F3, 37) (dual of [59060, 58818, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(34) [i] based on
- linear OA(3241, 59049, F3, 37) (dual of [59049, 58808, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(3231, 59049, F3, 35) (dual of [59049, 58818, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(31, 11, F3, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(36) ⊂ Ce(34) [i] based on
- discarding factors / shortening the dual code based on linear OA(3242, 59060, F3, 37) (dual of [59060, 58818, 38]-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(3242, 59059, F3, 37) (dual of [59059, 58817, 38]-code), using
- net defined by OOA [i] based on linear OOA(3242, 3281, F3, 37, 37) (dual of [(3281, 37), 121155, 38]-NRT-code), using
(206, 243, 19390)-Net over F3 — Digital
Digital (206, 243, 19390)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3243, 19390, F3, 3, 37) (dual of [(19390, 3), 57927, 38]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3243, 19687, F3, 3, 37) (dual of [(19687, 3), 58818, 38]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3243, 59061, F3, 37) (dual of [59061, 58818, 38]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3242, 59060, F3, 37) (dual of [59060, 58818, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(34) [i] based on
- linear OA(3241, 59049, F3, 37) (dual of [59049, 58808, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(3231, 59049, F3, 35) (dual of [59049, 58818, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(31, 11, F3, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(36) ⊂ Ce(34) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3242, 59060, F3, 37) (dual of [59060, 58818, 38]-code), using
- OOA 3-folding [i] based on linear OA(3243, 59061, F3, 37) (dual of [59061, 58818, 38]-code), using
- discarding factors / shortening the dual code based on linear OOA(3243, 19687, F3, 3, 37) (dual of [(19687, 3), 58818, 38]-NRT-code), using
(206, 243, large)-Net in Base 3 — Upper bound on s
There is no (206, 243, large)-net in base 3, because
- 35 times m-reduction [i] would yield (206, 208, large)-net in base 3, but