Best Known (39, 39+6, s)-Nets in Base 2
(39, 39+6, 16382)-Net over F2 — Constructive and digital
Digital (39, 45, 16382)-net over F2, using
- 21 times duplication [i] based on digital (38, 44, 16382)-net over F2, using
- net defined by OOA [i] based on linear OOA(244, 16382, F2, 6, 6) (dual of [(16382, 6), 98248, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(244, 16383, F2, 3, 6) (dual of [(16383, 3), 49105, 7]-NRT-code), using
- strength reduction [i] based on linear OOA(244, 16383, F2, 3, 7) (dual of [(16383, 3), 49105, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(244, 16383, F2, 3, 6) (dual of [(16383, 3), 49105, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(244, 16382, F2, 6, 6) (dual of [(16382, 6), 98248, 7]-NRT-code), using
(39, 39+6, 16384)-Net over F2 — Digital
Digital (39, 45, 16384)-net over F2, using
- net defined by OOA [i] based on linear OOA(245, 16384, F2, 6, 6) (dual of [(16384, 6), 98259, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(245, 16384, F2, 5, 6) (dual of [(16384, 5), 81875, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(245, 16384, F2, 2, 6) (dual of [(16384, 2), 32723, 7]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(243, 16383, F2, 2, 6) (dual of [(16383, 2), 32723, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(245, 16384, F2, 2, 6) (dual of [(16384, 2), 32723, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(245, 16384, F2, 5, 6) (dual of [(16384, 5), 81875, 7]-NRT-code), using
(39, 39+6, 59539)-Net in Base 2 — Upper bound on s
There is no (39, 45, 59540)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 35 185422 088311 > 245 [i]