Best Known (181−11, 181, s)-Nets in Base 2
(181−11, 181, 4718590)-Net over F2 — Constructive and digital
Digital (170, 181, 4718590)-net over F2, using
- 21 times duplication [i] based on digital (169, 180, 4718590)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (35, 40, 524289)-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
(181−11, 181, 4718599)-Net in Base 2 — Constructive
(170, 181, 4718599)-net in base 2, using
- (u, u+v)-construction [i] based on
- (36, 41, 524298)-net in base 2, using
- net defined by OOA [i] based on OOA(241, 524298, S2, 5, 5), using
- OOA 2-folding and stacking with additional row [i] based on OA(241, 1048597, S2, 5), using
- construction X4 applied to RM(1,20) ⊂ K(20) [i] based on
- OA(240, 1048576, S2, 5), using Kerdock OA K(20) [i]
- linear OA(221, 1048576, F2, 3) (dual of [1048576, 1048555, 4]-code or 1048576-cap in PG(20,2)), using Reed–Muller code RM(1,20) [i]
- linear OA(220, 21, F2, 19) (dual of [21, 1, 20]-code), using
- strength reduction [i] based on linear OA(220, 21, F2, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
- dual of repetition code with length 21 [i]
- strength reduction [i] based on linear OA(220, 21, F2, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
- linear OA(21, 21, F2, 1) (dual of [21, 20, 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(1,20) ⊂ K(20) [i] based on
- OOA 2-folding and stacking with additional row [i] based on OA(241, 1048597, S2, 5), using
- net defined by OOA [i] based on OOA(241, 524298, 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
- (36, 41, 524298)-net in base 2, using
(181−11, 181, large)-Net over F2 — Digital
Digital (170, 181, large)-net over F2, using
- 229 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
(181−11, 181, large)-Net in Base 2 — Upper bound on s
There is no (170, 181, large)-net in base 2, because
- 9 times m-reduction [i] would yield (170, 172, large)-net in base 2, but