Best Known (155, 196, s)-Nets in Base 2
(155, 196, 260)-Net over F2 — Constructive and digital
Digital (155, 196, 260)-net over F2, using
- t-expansion [i] based on digital (153, 196, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 49, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 49, 65)-net over F16, using
(155, 196, 465)-Net over F2 — Digital
Digital (155, 196, 465)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2196, 465, F2, 2, 41) (dual of [(465, 2), 734, 42]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2196, 512, F2, 2, 41) (dual of [(512, 2), 828, 42]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2196, 1024, F2, 41) (dual of [1024, 828, 42]-code), using
- an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- OOA 2-folding [i] based on linear OA(2196, 1024, F2, 41) (dual of [1024, 828, 42]-code), using
- discarding factors / shortening the dual code based on linear OOA(2196, 512, F2, 2, 41) (dual of [(512, 2), 828, 42]-NRT-code), using
(155, 196, 7121)-Net in Base 2 — Upper bound on s
There is no (155, 196, 7122)-net in base 2, because
- 1 times m-reduction [i] would yield (155, 195, 7122)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 50321 206355 890526 483324 022396 473921 777479 230359 402143 261696 > 2195 [i]