Best Known (166, 166+11, s)-Nets in Base 2
(166, 166+11, 4325374)-Net over F2 — Constructive and digital
Digital (166, 177, 4325374)-net over F2, using
- 21 times duplication [i] based on digital (165, 176, 4325374)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (31, 36, 131073)-net over F2, using
- digital (129, 140, 4194301)-net over F2, using
- net defined by OOA [i] based on linear OOA(2140, 4194301, F2, 15, 11) (dual of [(4194301, 15), 62914375, 12]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2140, large, F2, 3, 11), using
- net defined by OOA [i] based on linear OOA(2140, 4194301, F2, 15, 11) (dual of [(4194301, 15), 62914375, 12]-NRT-code), using
- (u, u+v)-construction [i] based on
(166, 166+11, 4325382)-Net in Base 2 — Constructive
(166, 177, 4325382)-net in base 2, using
- (u, u+v)-construction [i] based on
- (32, 37, 131081)-net in base 2, using
- net defined by OOA [i] based on OOA(237, 131081, S2, 5, 5), using
- OOA 2-folding and stacking with additional row [i] based on OA(237, 262163, S2, 5), using
- construction X4 applied to RM(1,18) ⊂ K(18) [i] based on
- OA(236, 262144, S2, 5), using Kerdock OA K(18) [i]
- linear OA(219, 262144, F2, 3) (dual of [262144, 262125, 4]-code or 262144-cap in PG(18,2)), using Reed–Muller code RM(1,18) [i]
- linear OA(218, 19, F2, 17) (dual of [19, 1, 18]-code), using
- strength reduction [i] based on linear OA(218, 19, F2, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,2)), using
- dual of repetition code with length 19 [i]
- strength reduction [i] based on linear OA(218, 19, F2, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,2)), using
- linear OA(21, 19, F2, 1) (dual of [19, 18, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X4 applied to RM(1,18) ⊂ K(18) [i] based on
- OOA 2-folding and stacking with additional row [i] based on OA(237, 262163, S2, 5), using
- net defined by OOA [i] based on OOA(237, 131081, S2, 5, 5), using
- digital (129, 140, 4194301)-net over F2, using
- net defined by OOA [i] based on linear OOA(2140, 4194301, F2, 15, 11) (dual of [(4194301, 15), 62914375, 12]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2140, large, F2, 3, 11), using
- net defined by OOA [i] based on linear OOA(2140, 4194301, F2, 15, 11) (dual of [(4194301, 15), 62914375, 12]-NRT-code), using
- (32, 37, 131081)-net in base 2, using
(166, 166+11, large)-Net over F2 — Digital
Digital (166, 177, large)-net over F2, using
- 225 times duplication [i] based on digital (141, 152, large)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2152, large, F2, 3, 11), using
- 4 times NRT-code embedding in larger space [i] based on linear OOA(2140, large, F2, 3, 11), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2152, large, F2, 3, 11), using
(166, 166+11, large)-Net in Base 2 — Upper bound on s
There is no (166, 177, large)-net in base 2, because
- 9 times m-reduction [i] would yield (166, 168, large)-net in base 2, but