Best Known (107, 120, s)-Nets in Base 3
(107, 120, 797168)-Net over F3 — Constructive and digital
Digital (107, 120, 797168)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (1, 7, 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
- a shift-net [i]
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- digital (100, 113, 797161)-net over F3, using
- net defined by OOA [i] based on linear OOA(3113, 797161, F3, 13, 13) (dual of [(797161, 13), 10362980, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3113, 4782967, F3, 13) (dual of [4782967, 4782854, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3113, 4782969, F3, 13) (dual of [4782969, 4782856, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(3113, 4782969, F3, 13) (dual of [4782969, 4782856, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3113, 4782967, F3, 13) (dual of [4782967, 4782854, 14]-code), using
- net defined by OOA [i] based on linear OOA(3113, 797161, F3, 13, 13) (dual of [(797161, 13), 10362980, 14]-NRT-code), using
- digital (1, 7, 7)-net over F3, using
(107, 120, 1594335)-Net over F3 — Digital
Digital (107, 120, 1594335)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3120, 1594335, F3, 3, 13) (dual of [(1594335, 3), 4782885, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3120, 4783005, F3, 13) (dual of [4783005, 4782885, 14]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3119, 4783004, F3, 13) (dual of [4783004, 4782885, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,4]) [i] based on
- linear OA(3113, 4782970, F3, 13) (dual of [4782970, 4782857, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(385, 4782970, F3, 9) (dual of [4782970, 4782885, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(36, 34, F3, 3) (dual of [34, 28, 4]-code or 34-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to C([0,6]) ⊂ C([0,4]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3119, 4783004, F3, 13) (dual of [4783004, 4782885, 14]-code), using
- OOA 3-folding [i] based on linear OA(3120, 4783005, F3, 13) (dual of [4783005, 4782885, 14]-code), using
(107, 120, large)-Net in Base 3 — Upper bound on s
There is no (107, 120, large)-net in base 3, because
- 11 times m-reduction [i] would yield (107, 109, large)-net in base 3, but