Best Known (96, 96+25, s)-Nets in Base 2
(96, 96+25, 196)-Net over F2 — Constructive and digital
Digital (96, 121, 196)-net over F2, using
- 21 times duplication [i] based on digital (95, 120, 196)-net over F2, using
- trace code for nets [i] based on digital (5, 30, 49)-net over F16, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 5 and N(F) ≥ 49, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- trace code for nets [i] based on digital (5, 30, 49)-net over F16, using
(96, 96+25, 354)-Net over F2 — Digital
Digital (96, 121, 354)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2121, 354, F2, 2, 25) (dual of [(354, 2), 587, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2121, 512, F2, 2, 25) (dual of [(512, 2), 903, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2121, 1024, F2, 25) (dual of [1024, 903, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- OOA 2-folding [i] based on linear OA(2121, 1024, F2, 25) (dual of [1024, 903, 26]-code), using
- discarding factors / shortening the dual code based on linear OOA(2121, 512, F2, 2, 25) (dual of [(512, 2), 903, 26]-NRT-code), using
(96, 96+25, 5398)-Net in Base 2 — Upper bound on s
There is no (96, 121, 5399)-net in base 2, because
- 1 times m-reduction [i] would yield (96, 120, 5399)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1 331262 021354 596428 550472 257154 824614 > 2120 [i]