Best Known (236−32, 236, s)-Nets in Base 2
(236−32, 236, 1062)-Net over F2 — Constructive and digital
Digital (204, 236, 1062)-net over F2, using
- 22 times duplication [i] based on digital (202, 234, 1062)-net over F2, using
- trace code for nets [i] based on digital (7, 39, 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
- trace code for nets [i] based on digital (7, 39, 177)-net over F64, using
(236−32, 236, 4107)-Net over F2 — Digital
Digital (204, 236, 4107)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2236, 4107, F2, 4, 32) (dual of [(4107, 4), 16192, 33]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2236, 16428, F2, 32) (dual of [16428, 16192, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(2236, 16431, F2, 32) (dual of [16431, 16195, 33]-code), using
- 1 times truncation [i] based on linear OA(2237, 16432, F2, 33) (dual of [16432, 16195, 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(212, 48, F2, 5) (dual of [48, 36, 6]-code), using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- extracting embedded orthogonal array [i] based on digital (7, 11, 47)-net over F2, using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- construction X applied to Ce(32) ⊂ Ce(26) [i] based on
- 1 times truncation [i] based on linear OA(2237, 16432, F2, 33) (dual of [16432, 16195, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(2236, 16431, F2, 32) (dual of [16431, 16195, 33]-code), using
- OOA 4-folding [i] based on linear OA(2236, 16428, F2, 32) (dual of [16428, 16192, 33]-code), using
(236−32, 236, 187359)-Net in Base 2 — Upper bound on s
There is no (204, 236, 187360)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 110428 685261 676907 541021 821006 453989 892684 942973 021390 329227 386173 052335 > 2236 [i]