Best Known (101, 101+18, s)-Nets in Base 3
(101, 101+18, 2195)-Net over F3 — Constructive and digital
Digital (101, 119, 2195)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (2, 11, 8)-net over F3, using
- net from sequence [i] based on digital (2, 7)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 2 and N(F) ≥ 8, using
- net from sequence [i] based on digital (2, 7)-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 (2, 11, 8)-net over F3, using
(101, 101+18, 11212)-Net over F3 — Digital
Digital (101, 119, 11212)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3119, 11212, F3, 18) (dual of [11212, 11093, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3119, 19730, F3, 18) (dual of [19730, 19611, 19]-code), using
- 1 times truncation [i] based on linear OA(3120, 19731, F3, 19) (dual of [19731, 19611, 20]-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(311, 47, F3, 5) (dual of [47, 36, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to C([0,9]) ⊂ C([0,6]) [i] based on
- 1 times truncation [i] based on linear OA(3120, 19731, F3, 19) (dual of [19731, 19611, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3119, 19730, F3, 18) (dual of [19730, 19611, 19]-code), using
(101, 101+18, 4220110)-Net in Base 3 — Upper bound on s
There is no (101, 119, 4220111)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 599 003925 541419 567300 751679 331478 749352 567007 170547 614607 > 3119 [i]