Best Known (100, 118, s)-Nets in Base 3
(100, 118, 2194)-Net over F3 — Constructive and digital
Digital (100, 118, 2194)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 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 (90, 108, 2187)-net over F3, using
- net defined by OOA [i] based on linear OOA(3108, 2187, F3, 18, 18) (dual of [(2187, 18), 39258, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(3108, 19683, F3, 18) (dual of [19683, 19575, 19]-code), using
- 1 times truncation [i] based on linear OA(3109, 19684, F3, 19) (dual of [19684, 19575, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(3109, 19684, F3, 19) (dual of [19684, 19575, 20]-code), using
- OA 9-folding and stacking [i] based on linear OA(3108, 19683, F3, 18) (dual of [19683, 19575, 19]-code), using
- net defined by OOA [i] based on linear OOA(3108, 2187, F3, 18, 18) (dual of [(2187, 18), 39258, 19]-NRT-code), using
- digital (1, 10, 7)-net over F3, using
(100, 118, 10467)-Net over F3 — Digital
Digital (100, 118, 10467)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3118, 10467, F3, 18) (dual of [10467, 10349, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3118, 19729, F3, 18) (dual of [19729, 19611, 19]-code), using
- construction X applied to C([0,9]) ⊂ C([0,6]) [i] based on
- linear OA(3109, 19684, F3, 19) (dual of [19684, 19575, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(373, 19684, F3, 13) (dual of [19684, 19611, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(39, 45, F3, 4) (dual of [45, 36, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- construction X applied to C([0,9]) ⊂ C([0,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3118, 19729, F3, 18) (dual of [19729, 19611, 19]-code), using
(100, 118, 3735168)-Net in Base 3 — Upper bound on s
There is no (100, 118, 3735169)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 199 667845 389276 234294 926439 180314 714450 181444 824325 976547 > 3118 [i]