Best Known (206, 206+30, s)-Nets in Base 3
(206, 206+30, 11816)-Net over F3 — Constructive and digital
Digital (206, 236, 11816)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (1, 16, 7)-net over F3, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 1 and N(F) ≥ 7, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- digital (190, 220, 11809)-net over F3, using
- net defined by OOA [i] based on linear OOA(3220, 11809, F3, 30, 30) (dual of [(11809, 30), 354050, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(3220, 177135, F3, 30) (dual of [177135, 176915, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(3220, 177147, F3, 30) (dual of [177147, 176927, 31]-code), using
- 1 times truncation [i] based on linear OA(3221, 177148, F3, 31) (dual of [177148, 176927, 32]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(3221, 177148, F3, 31) (dual of [177148, 176927, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(3220, 177147, F3, 30) (dual of [177147, 176927, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(3220, 177135, F3, 30) (dual of [177135, 176915, 31]-code), using
- net defined by OOA [i] based on linear OOA(3220, 11809, F3, 30, 30) (dual of [(11809, 30), 354050, 31]-NRT-code), using
- digital (1, 16, 7)-net over F3, using
(206, 206+30, 74521)-Net over F3 — Digital
Digital (206, 236, 74521)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3236, 74521, F3, 2, 30) (dual of [(74521, 2), 148806, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3236, 88608, F3, 2, 30) (dual of [(88608, 2), 176980, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3236, 177216, F3, 30) (dual of [177216, 176980, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, 177217, F3, 30) (dual of [177217, 176981, 31]-code), using
- 1 times truncation [i] based on linear OA(3237, 177218, F3, 31) (dual of [177218, 176981, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(22) [i] based on
- linear OA(3221, 177147, F3, 31) (dual of [177147, 176926, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3166, 177147, F3, 23) (dual of [177147, 176981, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(316, 71, F3, 7) (dual of [71, 55, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(316, 82, F3, 7) (dual of [82, 66, 8]-code), using
- construction X applied to Ce(30) ⊂ Ce(22) [i] based on
- 1 times truncation [i] based on linear OA(3237, 177218, F3, 31) (dual of [177218, 176981, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, 177217, F3, 30) (dual of [177217, 176981, 31]-code), using
- OOA 2-folding [i] based on linear OA(3236, 177216, F3, 30) (dual of [177216, 176980, 31]-code), using
- discarding factors / shortening the dual code based on linear OOA(3236, 88608, F3, 2, 30) (dual of [(88608, 2), 176980, 31]-NRT-code), using
(206, 206+30, large)-Net in Base 3 — Upper bound on s
There is no (206, 236, large)-net in base 3, because
- 28 times m-reduction [i] would yield (206, 208, large)-net in base 3, but