Best Known (215, 240, s)-Nets in Base 3
(215, 240, 398590)-Net over F3 — Constructive and digital
Digital (215, 240, 398590)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (3, 15, 10)-net over F3, using
- net from sequence [i] based on digital (3, 9)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 3 and N(F) ≥ 10, using
- net from sequence [i] based on digital (3, 9)-sequence over F3, using
- digital (200, 225, 398580)-net over F3, using
- net defined by OOA [i] based on linear OOA(3225, 398580, F3, 25, 25) (dual of [(398580, 25), 9964275, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3225, 4782961, F3, 25) (dual of [4782961, 4782736, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3225, 4782969, F3, 25) (dual of [4782969, 4782744, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(3225, 4782969, F3, 25) (dual of [4782969, 4782744, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3225, 4782961, F3, 25) (dual of [4782961, 4782736, 26]-code), using
- net defined by OOA [i] based on linear OOA(3225, 398580, F3, 25, 25) (dual of [(398580, 25), 9964275, 26]-NRT-code), using
- digital (3, 15, 10)-net over F3, using
(215, 240, 1195760)-Net over F3 — Digital
Digital (215, 240, 1195760)-net over F3, using
- 31 times duplication [i] based on digital (214, 239, 1195760)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3239, 1195760, F3, 4, 25) (dual of [(1195760, 4), 4782801, 26]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3239, 4783040, F3, 25) (dual of [4783040, 4782801, 26]-code), using
- 3 times code embedding in larger space [i] based on linear OA(3236, 4783037, F3, 25) (dual of [4783037, 4782801, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(3225, 4782970, F3, 25) (dual of [4782970, 4782745, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(3169, 4782970, F3, 19) (dual of [4782970, 4782801, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(311, 67, F3, 5) (dual of [67, 56, 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([0,12]) ⊂ C([0,9]) [i] based on
- 3 times code embedding in larger space [i] based on linear OA(3236, 4783037, F3, 25) (dual of [4783037, 4782801, 26]-code), using
- OOA 4-folding [i] based on linear OA(3239, 4783040, F3, 25) (dual of [4783040, 4782801, 26]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3239, 1195760, F3, 4, 25) (dual of [(1195760, 4), 4782801, 26]-NRT-code), using
(215, 240, large)-Net in Base 3 — Upper bound on s
There is no (215, 240, large)-net in base 3, because
- 23 times m-reduction [i] would yield (215, 217, large)-net in base 3, but