Best Known (46−10, 46, s)-Nets in Base 2
(46−10, 46, 104)-Net over F2 — Constructive and digital
Digital (36, 46, 104)-net over F2, using
- net defined by OOA [i] based on linear OOA(246, 104, F2, 10, 10) (dual of [(104, 10), 994, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(246, 520, F2, 10) (dual of [520, 474, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(246, 521, F2, 10) (dual of [521, 475, 11]-code), using
- 1 times truncation [i] based on linear OA(247, 522, F2, 11) (dual of [522, 475, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(246, 512, F2, 11) (dual of [512, 466, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(237, 512, F2, 9) (dual of [512, 475, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(21, 10, F2, 1) (dual of [10, 9, 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(10) ⊂ Ce(8) [i] based on
- 1 times truncation [i] based on linear OA(247, 522, F2, 11) (dual of [522, 475, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(246, 521, F2, 10) (dual of [521, 475, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(246, 520, F2, 10) (dual of [520, 474, 11]-code), using
(46−10, 46, 254)-Net over F2 — Digital
Digital (36, 46, 254)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(246, 254, F2, 2, 10) (dual of [(254, 2), 462, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(246, 260, F2, 2, 10) (dual of [(260, 2), 474, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(246, 520, F2, 10) (dual of [520, 474, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(246, 521, F2, 10) (dual of [521, 475, 11]-code), using
- 1 times truncation [i] based on linear OA(247, 522, F2, 11) (dual of [522, 475, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(246, 512, F2, 11) (dual of [512, 466, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(237, 512, F2, 9) (dual of [512, 475, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(21, 10, F2, 1) (dual of [10, 9, 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(10) ⊂ Ce(8) [i] based on
- 1 times truncation [i] based on linear OA(247, 522, F2, 11) (dual of [522, 475, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(246, 521, F2, 10) (dual of [521, 475, 11]-code), using
- OOA 2-folding [i] based on linear OA(246, 520, F2, 10) (dual of [520, 474, 11]-code), using
- discarding factors / shortening the dual code based on linear OOA(246, 260, F2, 2, 10) (dual of [(260, 2), 474, 11]-NRT-code), using
(46−10, 46, 1525)-Net in Base 2 — Upper bound on s
There is no (36, 46, 1526)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 70 552134 921087 > 246 [i]