Best Known (221−38, 221, s)-Nets in Base 2
(221−38, 221, 380)-Net over F2 — Constructive and digital
Digital (183, 221, 380)-net over F2, using
- 21 times duplication [i] based on digital (182, 220, 380)-net over F2, using
- t-expansion [i] based on digital (181, 220, 380)-net over F2, using
- trace code for nets [i] based on digital (5, 44, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- trace code for nets [i] based on digital (5, 44, 76)-net over F32, using
- t-expansion [i] based on digital (181, 220, 380)-net over F2, using
(221−38, 221, 1014)-Net over F2 — Digital
Digital (183, 221, 1014)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2221, 1014, F2, 2, 38) (dual of [(1014, 2), 1807, 39]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2221, 1046, F2, 2, 38) (dual of [(1046, 2), 1871, 39]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2221, 2092, F2, 38) (dual of [2092, 1871, 39]-code), using
- 1 times truncation [i] based on linear OA(2222, 2093, F2, 39) (dual of [2093, 1871, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(32) [i] based on
- linear OA(2210, 2048, F2, 39) (dual of [2048, 1838, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2177, 2048, F2, 33) (dual of [2048, 1871, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(212, 45, F2, 5) (dual of [45, 33, 6]-code), using
- discarding factors / shortening the dual code based on 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
- discarding factors / shortening the dual code based on linear OA(212, 48, F2, 5) (dual of [48, 36, 6]-code), using
- construction X applied to Ce(38) ⊂ Ce(32) [i] based on
- 1 times truncation [i] based on linear OA(2222, 2093, F2, 39) (dual of [2093, 1871, 40]-code), using
- OOA 2-folding [i] based on linear OA(2221, 2092, F2, 38) (dual of [2092, 1871, 39]-code), using
- discarding factors / shortening the dual code based on linear OOA(2221, 1046, F2, 2, 38) (dual of [(1046, 2), 1871, 39]-NRT-code), using
(221−38, 221, 25129)-Net in Base 2 — Upper bound on s
There is no (183, 221, 25130)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 3 370907 772487 800728 753233 119749 117271 378821 094215 282268 075254 669808 > 2221 [i]