Best Known (187, 210, s)-Nets in Base 2
(187, 210, 47662)-Net over F2 — Constructive and digital
Digital (187, 210, 47662)-net over F2, using
- net defined by OOA [i] based on linear OOA(2210, 47662, F2, 23, 23) (dual of [(47662, 23), 1096016, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2210, 524283, F2, 23) (dual of [524283, 524073, 24]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(2210, 524288, F2, 23) (dual of [524288, 524078, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2210, 524283, F2, 23) (dual of [524283, 524073, 24]-code), using
(187, 210, 74898)-Net over F2 — Digital
Digital (187, 210, 74898)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2210, 74898, F2, 7, 23) (dual of [(74898, 7), 524076, 24]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2210, 524286, F2, 23) (dual of [524286, 524076, 24]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(2210, 524288, F2, 23) (dual of [524288, 524078, 24]-code), using
- OOA 7-folding [i] based on linear OA(2210, 524286, F2, 23) (dual of [524286, 524076, 24]-code), using
(187, 210, 2573838)-Net in Base 2 — Upper bound on s
There is no (187, 210, 2573839)-net in base 2, because
- 1 times m-reduction [i] would yield (187, 209, 2573839)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 822 752344 359939 309039 349179 970064 674405 416583 067464 764100 020450 > 2209 [i]