Best Known (178, 200, s)-Nets in Base 2
(178, 200, 23833)-Net over F2 — Constructive and digital
Digital (178, 200, 23833)-net over F2, using
- net defined by OOA [i] based on linear OOA(2200, 23833, F2, 22, 22) (dual of [(23833, 22), 524126, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2200, 262163, F2, 22) (dual of [262163, 261963, 23]-code), using
- strength reduction [i] based on linear OA(2200, 262163, F2, 23) (dual of [262163, 261963, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- linear OA(2199, 262144, F2, 23) (dual of [262144, 261945, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2181, 262144, F2, 21) (dual of [262144, 261963, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(21, 19, F2, 1) (dual of [19, 18, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- strength reduction [i] based on linear OA(2200, 262163, F2, 23) (dual of [262163, 261963, 24]-code), using
- OA 11-folding and stacking [i] based on linear OA(2200, 262163, F2, 22) (dual of [262163, 261963, 23]-code), using
(178, 200, 43693)-Net over F2 — Digital
Digital (178, 200, 43693)-net over F2, using
- 21 times duplication [i] based on digital (177, 199, 43693)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2199, 43693, F2, 6, 22) (dual of [(43693, 6), 261959, 23]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2199, 262158, F2, 22) (dual of [262158, 261959, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2199, 262162, F2, 22) (dual of [262162, 261963, 23]-code), using
- 1 times truncation [i] based on linear OA(2200, 262163, F2, 23) (dual of [262163, 261963, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- linear OA(2199, 262144, F2, 23) (dual of [262144, 261945, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2181, 262144, F2, 21) (dual of [262144, 261963, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(21, 19, F2, 1) (dual of [19, 18, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- 1 times truncation [i] based on linear OA(2200, 262163, F2, 23) (dual of [262163, 261963, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2199, 262162, F2, 22) (dual of [262162, 261963, 23]-code), using
- OOA 6-folding [i] based on linear OA(2199, 262158, F2, 22) (dual of [262158, 261959, 23]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2199, 43693, F2, 6, 22) (dual of [(43693, 6), 261959, 23]-NRT-code), using
(178, 200, 1459761)-Net in Base 2 — Upper bound on s
There is no (178, 200, 1459762)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 606938 433390 147363 051640 089174 097041 697740 696013 679622 370144 > 2200 [i]