Best Known (112−14, 112, s)-Nets in Base 2
(112−14, 112, 9362)-Net over F2 — Constructive and digital
Digital (98, 112, 9362)-net over F2, using
- net defined by OOA [i] based on linear OOA(2112, 9362, F2, 14, 14) (dual of [(9362, 14), 130956, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2112, 65534, F2, 14) (dual of [65534, 65422, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2112, 65535, F2, 14) (dual of [65535, 65423, 15]-code), using
- 1 times truncation [i] based on linear OA(2113, 65536, F2, 15) (dual of [65536, 65423, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 1 times truncation [i] based on linear OA(2113, 65536, F2, 15) (dual of [65536, 65423, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2112, 65535, F2, 14) (dual of [65535, 65423, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(2112, 65534, F2, 14) (dual of [65534, 65422, 15]-code), using
(112−14, 112, 16383)-Net over F2 — Digital
Digital (98, 112, 16383)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2112, 16383, F2, 4, 14) (dual of [(16383, 4), 65420, 15]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2112, 65532, F2, 14) (dual of [65532, 65420, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2112, 65535, F2, 14) (dual of [65535, 65423, 15]-code), using
- 1 times truncation [i] based on linear OA(2113, 65536, F2, 15) (dual of [65536, 65423, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 1 times truncation [i] based on linear OA(2113, 65536, F2, 15) (dual of [65536, 65423, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2112, 65535, F2, 14) (dual of [65535, 65423, 15]-code), using
- OOA 4-folding [i] based on linear OA(2112, 65532, F2, 14) (dual of [65532, 65420, 15]-code), using
(112−14, 112, 221502)-Net in Base 2 — Upper bound on s
There is no (98, 112, 221503)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 5192 350403 717739 407978 152593 768346 > 2112 [i]