Best Known (232−23, 232, s)-Nets in Base 2
(232−23, 232, 190650)-Net over F2 — Constructive and digital
Digital (209, 232, 190650)-net over F2, using
- net defined by OOA [i] based on linear OOA(2232, 190650, F2, 23, 23) (dual of [(190650, 23), 4384718, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2232, 2097151, F2, 23) (dual of [2097151, 2096919, 24]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- OOA 11-folding and stacking with additional row [i] based on linear OA(2232, 2097151, F2, 23) (dual of [2097151, 2096919, 24]-code), using
(232−23, 232, 262144)-Net over F2 — Digital
Digital (209, 232, 262144)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2232, 262144, F2, 8, 23) (dual of [(262144, 8), 2096920, 24]-NRT-code), using
- OOA 8-folding [i] based on linear OA(2232, 2097152, F2, 23) (dual of [2097152, 2096920, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- OOA 8-folding [i] based on linear OA(2232, 2097152, F2, 23) (dual of [2097152, 2096920, 24]-code), using
(232−23, 232, large)-Net in Base 2 — Upper bound on s
There is no (209, 232, large)-net in base 2, because
- 21 times m-reduction [i] would yield (209, 211, large)-net in base 2, but