Best Known (105−14, 105, s)-Nets in Base 2
(105−14, 105, 4681)-Net over F2 — Constructive and digital
Digital (91, 105, 4681)-net over F2, using
- net defined by OOA [i] based on linear OOA(2105, 4681, F2, 14, 14) (dual of [(4681, 14), 65429, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2105, 32767, F2, 14) (dual of [32767, 32662, 15]-code), using
- the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- OA 7-folding and stacking [i] based on linear OA(2105, 32767, F2, 14) (dual of [32767, 32662, 15]-code), using
(105−14, 105, 8191)-Net over F2 — Digital
Digital (91, 105, 8191)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2105, 8191, F2, 4, 14) (dual of [(8191, 4), 32659, 15]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2105, 32764, F2, 14) (dual of [32764, 32659, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2105, 32767, F2, 14) (dual of [32767, 32662, 15]-code), using
- the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(2105, 32767, F2, 14) (dual of [32767, 32662, 15]-code), using
- OOA 4-folding [i] based on linear OA(2105, 32764, F2, 14) (dual of [32764, 32659, 15]-code), using
(105−14, 105, 110746)-Net in Base 2 — Upper bound on s
There is no (91, 105, 110747)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 40 566518 678698 923108 552956 139708 > 2105 [i]