Best Known (109, 109+8, s)-Nets in Base 2
(109, 109+8, 4194301)-Net over F2 — Constructive and digital
Digital (109, 117, 4194301)-net over F2, using
- 21 times duplication [i] based on digital (108, 116, 4194301)-net over F2, using
- t-expansion [i] based on digital (107, 116, 4194301)-net over F2, using
- net defined by OOA [i] based on linear OOA(2116, 4194301, F2, 9, 9) (dual of [(4194301, 9), 37748593, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(2116, 4194301, F2, 8, 9) (dual of [(4194301, 8), 33554292, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2116, large, F2, 2, 9), using
- appending kth column [i] based on linear OOA(2116, 4194301, F2, 8, 9) (dual of [(4194301, 8), 33554292, 10]-NRT-code), using
- net defined by OOA [i] based on linear OOA(2116, 4194301, F2, 9, 9) (dual of [(4194301, 9), 37748593, 10]-NRT-code), using
- t-expansion [i] based on digital (107, 116, 4194301)-net over F2, using
(109, 109+8, large)-Net over F2 — Digital
Digital (109, 117, large)-net over F2, using
- t-expansion [i] based on digital (108, 117, large)-net over F2, using
- net defined by OOA [i] based on linear OOA(2117, large, F2, 9, 9), using
- appending kth column [i] based on linear OOA(2117, large, F2, 8, 9), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2117, large, F2, 3, 9), using
- appending kth column [i] based on linear OOA(2117, large, F2, 8, 9), using
- net defined by OOA [i] based on linear OOA(2117, large, F2, 9, 9), using
(109, 109+8, large)-Net in Base 2 — Upper bound on s
There is no (109, 117, large)-net in base 2, because
- 6 times m-reduction [i] would yield (109, 111, large)-net in base 2, but