Best Known (250−34, 250, s)-Nets in Base 2
(250−34, 250, 1062)-Net over F2 — Constructive and digital
Digital (216, 250, 1062)-net over F2, using
- 24 times duplication [i] based on digital (212, 246, 1062)-net over F2, using
- trace code for nets [i] based on digital (7, 41, 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, 41, 177)-net over F64, using
(250−34, 250, 4107)-Net over F2 — Digital
Digital (216, 250, 4107)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2250, 4107, F2, 4, 34) (dual of [(4107, 4), 16178, 35]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2250, 16428, F2, 34) (dual of [16428, 16178, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(2250, 16431, F2, 34) (dual of [16431, 16181, 35]-code), using
- 1 times truncation [i] based on linear OA(2251, 16432, F2, 35) (dual of [16432, 16181, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(28) [i] based on
- linear OA(2239, 16384, F2, 35) (dual of [16384, 16145, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2197, 16384, F2, 29) (dual of [16384, 16187, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(34) ⊂ Ce(28) [i] based on
- 1 times truncation [i] based on linear OA(2251, 16432, F2, 35) (dual of [16432, 16181, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(2250, 16431, F2, 34) (dual of [16431, 16181, 35]-code), using
- OOA 4-folding [i] based on linear OA(2250, 16428, F2, 34) (dual of [16428, 16178, 35]-code), using
(250−34, 250, 191778)-Net in Base 2 — Upper bound on s
There is no (216, 250, 191779)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1809 304433 792925 566495 504139 807990 371088 624067 793491 323424 321883 883367 401592 > 2250 [i]