Best Known (80, 91, s)-Nets in Base 2
(80, 91, 52428)-Net over F2 — Constructive and digital
Digital (80, 91, 52428)-net over F2, using
- net defined by OOA [i] based on linear OOA(291, 52428, F2, 11, 11) (dual of [(52428, 11), 576617, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(291, 262141, F2, 11) (dual of [262141, 262050, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(291, 262144, F2, 11) (dual of [262144, 262053, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(291, 262144, F2, 11) (dual of [262144, 262053, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(291, 262141, F2, 11) (dual of [262141, 262050, 12]-code), using
(80, 91, 65536)-Net over F2 — Digital
Digital (80, 91, 65536)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(291, 65536, F2, 4, 11) (dual of [(65536, 4), 262053, 12]-NRT-code), using
- OOA 4-folding [i] based on linear OA(291, 262144, F2, 11) (dual of [262144, 262053, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 4-folding [i] based on linear OA(291, 262144, F2, 11) (dual of [262144, 262053, 12]-code), using
(80, 91, 682922)-Net in Base 2 — Upper bound on s
There is no (80, 91, 682923)-net in base 2, because
- 1 times m-reduction [i] would yield (80, 90, 682923)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1237 940321 542451 700287 049536 > 290 [i]