Best Known (92, 119, s)-Nets in Base 2
(92, 119, 144)-Net over F2 — Constructive and digital
Digital (92, 119, 144)-net over F2, using
- t-expansion [i] based on digital (91, 119, 144)-net over F2, using
- 1 times m-reduction [i] based on digital (91, 120, 144)-net over F2, using
- trace code for nets [i] based on digital (11, 40, 48)-net over F8, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 11 and N(F) ≥ 48, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- trace code for nets [i] based on digital (11, 40, 48)-net over F8, using
- 1 times m-reduction [i] based on digital (91, 120, 144)-net over F2, using
(92, 119, 255)-Net over F2 — Digital
Digital (92, 119, 255)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2119, 255, F2, 2, 27) (dual of [(255, 2), 391, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2119, 261, F2, 2, 27) (dual of [(261, 2), 403, 28]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2119, 522, F2, 27) (dual of [522, 403, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- linear OA(2118, 512, F2, 27) (dual of [512, 394, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2109, 512, F2, 25) (dual of [512, 403, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(21, 10, F2, 1) (dual of [10, 9, 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 X applied to Ce(26) ⊂ Ce(24) [i] based on
- OOA 2-folding [i] based on linear OA(2119, 522, F2, 27) (dual of [522, 403, 28]-code), using
- discarding factors / shortening the dual code based on linear OOA(2119, 261, F2, 2, 27) (dual of [(261, 2), 403, 28]-NRT-code), using
(92, 119, 3041)-Net in Base 2 — Upper bound on s
There is no (92, 119, 3042)-net in base 2, because
- 1 times m-reduction [i] would yield (92, 118, 3042)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 332540 912602 037554 847363 689302 702600 > 2118 [i]