Best Known (205, 205+32, s)-Nets in Base 2
(205, 205+32, 1062)-Net over F2 — Constructive and digital
Digital (205, 237, 1062)-net over F2, using
- 23 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
(205, 205+32, 4109)-Net over F2 — Digital
Digital (205, 237, 4109)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2237, 4109, F2, 4, 32) (dual of [(4109, 4), 16199, 33]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2237, 16436, F2, 32) (dual of [16436, 16199, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(2237, 16438, F2, 32) (dual of [16438, 16201, 33]-code), using
- 1 times truncation [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 truncation [i] based on linear OA(2238, 16439, F2, 33) (dual of [16439, 16201, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(2237, 16438, F2, 32) (dual of [16438, 16201, 33]-code), using
- OOA 4-folding [i] based on linear OA(2237, 16436, F2, 32) (dual of [16436, 16199, 33]-code), using
(205, 205+32, 195656)-Net in Base 2 — Upper bound on s
There is no (205, 237, 195657)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 220872 247855 212197 457395 311433 555111 481362 153241 551490 750719 456779 451700 > 2237 [i]