Best Known (108, 116, s)-Nets in Base 2
(108, 116, 4194301)-Net over F2 — Constructive and digital
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
(108, 116, large)-Net over F2 — Digital
Digital (108, 116, large)-net over F2, using
- 1 times m-reduction [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
(108, 116, large)-Net in Base 2 — Upper bound on s
There is no (108, 116, large)-net in base 2, because
- 6 times m-reduction [i] would yield (108, 110, large)-net in base 2, but