Best Known (187, 209, s)-Nets in Base 2
(187, 209, 47662)-Net over F2 — Constructive and digital
Digital (187, 209, 47662)-net over F2, using
- net defined by OOA [i] based on linear OOA(2209, 47662, F2, 22, 22) (dual of [(47662, 22), 1048355, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2209, 524282, F2, 22) (dual of [524282, 524073, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2209, 524287, F2, 22) (dual of [524287, 524078, 23]-code), using
- 1 times truncation [i] based on linear OA(2210, 524288, F2, 23) (dual of [524288, 524078, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 1 times truncation [i] based on linear OA(2210, 524288, F2, 23) (dual of [524288, 524078, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2209, 524287, F2, 22) (dual of [524287, 524078, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(2209, 524282, F2, 22) (dual of [524282, 524073, 23]-code), using
(187, 209, 76135)-Net over F2 — Digital
Digital (187, 209, 76135)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2209, 76135, F2, 6, 22) (dual of [(76135, 6), 456601, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2209, 87381, F2, 6, 22) (dual of [(87381, 6), 524077, 23]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2209, 524286, F2, 22) (dual of [524286, 524077, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2209, 524287, F2, 22) (dual of [524287, 524078, 23]-code), using
- 1 times truncation [i] based on linear OA(2210, 524288, F2, 23) (dual of [524288, 524078, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 1 times truncation [i] based on linear OA(2210, 524288, F2, 23) (dual of [524288, 524078, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2209, 524287, F2, 22) (dual of [524287, 524078, 23]-code), using
- OOA 6-folding [i] based on linear OA(2209, 524286, F2, 22) (dual of [524286, 524077, 23]-code), using
- discarding factors / shortening the dual code based on linear OOA(2209, 87381, F2, 6, 22) (dual of [(87381, 6), 524077, 23]-NRT-code), using
(187, 209, 2573838)-Net in Base 2 — Upper bound on s
There is no (187, 209, 2573839)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 822 752344 359939 309039 349179 970064 674405 416583 067464 764100 020450 > 2209 [i]