Best Known (211, 247, s)-Nets in Base 2
(211, 247, 768)-Net over F2 — Constructive and digital
Digital (211, 247, 768)-net over F2, using
- 21 times duplication [i] based on digital (210, 246, 768)-net over F2, using
- trace code for nets [i] based on digital (5, 41, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- trace code for nets [i] based on digital (5, 41, 128)-net over F64, using
(211, 247, 2478)-Net over F2 — Digital
Digital (211, 247, 2478)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2247, 2478, F2, 3, 36) (dual of [(2478, 3), 7187, 37]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2247, 2747, F2, 3, 36) (dual of [(2747, 3), 7994, 37]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2247, 8241, F2, 36) (dual of [8241, 7994, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(2247, 8243, F2, 36) (dual of [8243, 7996, 37]-code), using
- 1 times truncation [i] based on linear OA(2248, 8244, F2, 37) (dual of [8244, 7996, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(30) [i] based on
- linear OA(2235, 8192, F2, 37) (dual of [8192, 7957, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2196, 8192, F2, 31) (dual of [8192, 7996, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(213, 52, F2, 5) (dual of [52, 39, 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(36) ⊂ Ce(30) [i] based on
- 1 times truncation [i] based on linear OA(2248, 8244, F2, 37) (dual of [8244, 7996, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(2247, 8243, F2, 36) (dual of [8243, 7996, 37]-code), using
- OOA 3-folding [i] based on linear OA(2247, 8241, F2, 36) (dual of [8241, 7994, 37]-code), using
- discarding factors / shortening the dual code based on linear OOA(2247, 2747, F2, 3, 36) (dual of [(2747, 3), 7994, 37]-NRT-code), using
(211, 247, 102051)-Net in Base 2 — Upper bound on s
There is no (211, 247, 102052)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 226 191236 048353 189518 146569 251983 699383 648699 019981 920826 643740 096477 378890 > 2247 [i]