Best Known (200−23, 200, s)-Nets in Base 2
(200−23, 200, 23832)-Net over F2 — Constructive and digital
Digital (177, 200, 23832)-net over F2, using
- net defined by OOA [i] based on linear OOA(2200, 23832, F2, 23, 23) (dual of [(23832, 23), 547936, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2200, 262153, F2, 23) (dual of [262153, 261953, 24]-code), using
- discarding factors / shortening the dual code 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
- discarding factors / shortening the dual code based on linear OA(2200, 262163, F2, 23) (dual of [262163, 261963, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2200, 262153, F2, 23) (dual of [262153, 261953, 24]-code), using
(200−23, 200, 37451)-Net over F2 — Digital
Digital (177, 200, 37451)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2200, 37451, F2, 7, 23) (dual of [(37451, 7), 261957, 24]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2200, 262157, F2, 23) (dual of [262157, 261957, 24]-code), using
- discarding factors / shortening the dual code 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
- discarding factors / shortening the dual code based on linear OA(2200, 262163, F2, 23) (dual of [262163, 261963, 24]-code), using
- OOA 7-folding [i] based on linear OA(2200, 262157, F2, 23) (dual of [262157, 261957, 24]-code), using
(200−23, 200, 1370614)-Net in Base 2 — Upper bound on s
There is no (177, 200, 1370615)-net in base 2, because
- 1 times m-reduction [i] would yield (177, 199, 1370615)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 803471 235553 273154 467924 365571 091196 829665 284816 498947 247748 > 2199 [i]