Best Known (36, 41, s)-Nets in Base 2
(36, 41, 524289)-Net over F2 — Constructive and digital
Digital (36, 41, 524289)-net over F2, using
- 21 times duplication [i] based on digital (35, 40, 524289)-net over F2, using
(36, 41, 524298)-Net in Base 2 — Constructive
(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
(36, 41, 1482907)-Net in Base 2 — Upper bound on s
There is no (36, 41, 1482908)-net in base 2, because
- 1 times m-reduction [i] would yield (36, 40, 1482908)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1 099511 775503 > 240 [i]