Best Known (40−10, 40, s)-Nets in Base 2
(40−10, 40, 72)-Net over F2 — Constructive and digital
Digital (30, 40, 72)-net over F2, using
- 21 times duplication [i] based on digital (29, 39, 72)-net over F2, using
- trace code for nets [i] based on digital (3, 13, 24)-net over F8, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- trace code for nets [i] based on digital (3, 13, 24)-net over F8, using
(40−10, 40, 128)-Net over F2 — Digital
Digital (30, 40, 128)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(240, 128, F2, 2, 10) (dual of [(128, 2), 216, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(240, 256, F2, 10) (dual of [256, 216, 11]-code), using
- a “Gp†code from Brouwer’s database [i]
- OOA 2-folding [i] based on linear OA(240, 256, F2, 10) (dual of [256, 216, 11]-code), using
(40−10, 40, 659)-Net in Base 2 — Upper bound on s
There is no (30, 40, 660)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 099881 388508 > 240 [i]