Best Known (212, 240, s)-Nets in Base 2
(212, 240, 9363)-Net over F2 — Constructive and digital
Digital (212, 240, 9363)-net over F2, using
- t-expansion [i] based on digital (211, 240, 9363)-net over F2, using
- net defined by OOA [i] based on linear OOA(2240, 9363, F2, 29, 29) (dual of [(9363, 29), 271287, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2240, 131083, F2, 29) (dual of [131083, 130843, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2240, 131090, F2, 29) (dual of [131090, 130850, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- linear OA(2239, 131072, F2, 29) (dual of [131072, 130833, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2222, 131072, F2, 27) (dual of [131072, 130850, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(21, 18, F2, 1) (dual of [18, 17, 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(28) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(2240, 131090, F2, 29) (dual of [131090, 130850, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2240, 131083, F2, 29) (dual of [131083, 130843, 30]-code), using
- net defined by OOA [i] based on linear OOA(2240, 9363, F2, 29, 29) (dual of [(9363, 29), 271287, 30]-NRT-code), using
(212, 240, 19595)-Net over F2 — Digital
Digital (212, 240, 19595)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2240, 19595, F2, 6, 28) (dual of [(19595, 6), 117330, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2240, 21848, F2, 6, 28) (dual of [(21848, 6), 130848, 29]-NRT-code), using
- strength reduction [i] based on linear OOA(2240, 21848, F2, 6, 29) (dual of [(21848, 6), 130848, 30]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2240, 131088, F2, 29) (dual of [131088, 130848, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2240, 131090, F2, 29) (dual of [131090, 130850, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- linear OA(2239, 131072, F2, 29) (dual of [131072, 130833, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2222, 131072, F2, 27) (dual of [131072, 130850, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(21, 18, F2, 1) (dual of [18, 17, 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(28) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(2240, 131090, F2, 29) (dual of [131090, 130850, 30]-code), using
- OOA 6-folding [i] based on linear OA(2240, 131088, F2, 29) (dual of [131088, 130848, 30]-code), using
- strength reduction [i] based on linear OOA(2240, 21848, F2, 6, 29) (dual of [(21848, 6), 130848, 30]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2240, 21848, F2, 6, 28) (dual of [(21848, 6), 130848, 29]-NRT-code), using
(212, 240, 874906)-Net in Base 2 — Upper bound on s
There is no (212, 240, 874907)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 766853 683566 085455 670295 058784 406189 590499 370006 829402 810260 874075 482244 > 2240 [i]