Best Known (117, 139, s)-Nets in Base 3
(117, 139, 1796)-Net over F3 — Constructive and digital
Digital (117, 139, 1796)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 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 (105, 127, 1789)-net over F3, using
- net defined by OOA [i] based on linear OOA(3127, 1789, F3, 22, 22) (dual of [(1789, 22), 39231, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3127, 19679, F3, 22) (dual of [19679, 19552, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3127, 19683, F3, 22) (dual of [19683, 19556, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(3127, 19683, F3, 22) (dual of [19683, 19556, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3127, 19679, F3, 22) (dual of [19679, 19552, 23]-code), using
- net defined by OOA [i] based on linear OOA(3127, 1789, F3, 22, 22) (dual of [(1789, 22), 39231, 23]-NRT-code), using
- digital (1, 12, 7)-net over F3, using
(117, 139, 9865)-Net over F3 — Digital
Digital (117, 139, 9865)-net over F3, using
- 31 times duplication [i] based on digital (116, 138, 9865)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3138, 9865, F3, 2, 22) (dual of [(9865, 2), 19592, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3138, 19730, F3, 22) (dual of [19730, 19592, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(3127, 19683, F3, 22) (dual of [19683, 19556, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(391, 19683, F3, 16) (dual of [19683, 19592, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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 Ce(21) ⊂ Ce(15) [i] based on
- OOA 2-folding [i] based on linear OA(3138, 19730, F3, 22) (dual of [19730, 19592, 23]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3138, 9865, F3, 2, 22) (dual of [(9865, 2), 19592, 23]-NRT-code), using
(117, 139, 2624581)-Net in Base 3 — Upper bound on s
There is no (117, 139, 2624582)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2 088598 454483 987485 357385 714066 695705 379061 432006 636399 409772 850705 > 3139 [i]