Best Known (35, 46, s)-Nets in Base 2
(35, 46, 102)-Net over F2 — Constructive and digital
Digital (35, 46, 102)-net over F2, using
- net defined by OOA [i] based on linear OOA(246, 102, F2, 11, 11) (dual of [(102, 11), 1076, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(246, 511, F2, 11) (dual of [511, 465, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- OOA 5-folding and stacking with additional row [i] based on linear OA(246, 511, F2, 11) (dual of [511, 465, 12]-code), using
(35, 46, 170)-Net over F2 — Digital
Digital (35, 46, 170)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(246, 170, F2, 3, 11) (dual of [(170, 3), 464, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(246, 510, F2, 11) (dual of [510, 464, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(246, 511, F2, 11) (dual of [511, 465, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(246, 511, F2, 11) (dual of [511, 465, 12]-code), using
- OOA 3-folding [i] based on linear OA(246, 510, F2, 11) (dual of [510, 464, 12]-code), using
(35, 46, 1326)-Net in Base 2 — Upper bound on s
There is no (35, 46, 1327)-net in base 2, because
- 1 times m-reduction [i] would yield (35, 45, 1327)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 35 202404 683452 > 245 [i]