Best Known (30, 30+6, s)-Nets in Base 2
(30, 30+6, 2047)-Net over F2 — Constructive and digital
Digital (30, 36, 2047)-net over F2, using
- 21 times duplication [i] based on digital (29, 35, 2047)-net over F2, using
- t-expansion [i] based on digital (28, 35, 2047)-net over F2, using
(30, 30+6, 2048)-Net over F2 — Digital
Digital (30, 36, 2048)-net over F2, using
- net defined by OOA [i] based on linear OOA(236, 2048, F2, 6, 6) (dual of [(2048, 6), 12252, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(236, 2048, F2, 5, 6) (dual of [(2048, 5), 10204, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(236, 2048, F2, 2, 6) (dual of [(2048, 2), 4060, 7]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(234, 2047, F2, 2, 6) (dual of [(2047, 2), 4060, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (28, 34, 2047)-net over F2, using
- 1 times m-reduction [i] based on digital (28, 35, 2047)-net over F2, using
- extracting embedded OOA [i] based on digital (28, 34, 2047)-net over F2, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(234, 2047, F2, 2, 6) (dual of [(2047, 2), 4060, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(236, 2048, F2, 2, 6) (dual of [(2048, 2), 4060, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(236, 2048, F2, 5, 6) (dual of [(2048, 5), 10204, 7]-NRT-code), using
(30, 30+6, 7438)-Net in Base 2 — Upper bound on s
There is no (30, 36, 7439)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 68721 504318 > 236 [i]