Best Known (207, 207+33, s)-Nets in Base 2
(207, 207+33, 1062)-Net over F2 — Constructive and digital
Digital (207, 240, 1062)-net over F2, using
- trace code for nets [i] based on digital (7, 40, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
(207, 207+33, 3852)-Net over F2 — Digital
Digital (207, 240, 3852)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2240, 3852, F2, 4, 33) (dual of [(3852, 4), 15168, 34]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2240, 4110, F2, 4, 33) (dual of [(4110, 4), 16200, 34]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2239, 4110, F2, 4, 33) (dual of [(4110, 4), 16201, 34]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2239, 16440, F2, 33) (dual of [16440, 16201, 34]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2238, 16439, F2, 33) (dual of [16439, 16201, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(26) [i] based on
- linear OA(2225, 16384, F2, 33) (dual of [16384, 16159, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2183, 16384, F2, 27) (dual of [16384, 16201, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(213, 55, F2, 5) (dual of [55, 42, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using
- construction X applied to Ce(32) ⊂ Ce(26) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2238, 16439, F2, 33) (dual of [16439, 16201, 34]-code), using
- OOA 4-folding [i] based on linear OA(2239, 16440, F2, 33) (dual of [16440, 16201, 34]-code), using
- 21 times duplication [i] based on linear OOA(2239, 4110, F2, 4, 33) (dual of [(4110, 4), 16201, 34]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2240, 4110, F2, 4, 33) (dual of [(4110, 4), 16200, 34]-NRT-code), using
(207, 207+33, 213366)-Net in Base 2 — Upper bound on s
There is no (207, 240, 213367)-net in base 2, because
- 1 times m-reduction [i] would yield (207, 239, 213367)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 883449 367925 686970 893080 184260 902876 624068 901764 239186 279835 881306 986439 > 2239 [i]