Best Known (178−38, 178, s)-Nets in Base 2
(178−38, 178, 260)-Net over F2 — Constructive and digital
Digital (140, 178, 260)-net over F2, using
- 22 times duplication [i] based on digital (138, 176, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 44, 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, 44, 65)-net over F16, using
(178−38, 178, 389)-Net over F2 — Digital
Digital (140, 178, 389)-net over F2, using
(178−38, 178, 5212)-Net in Base 2 — Upper bound on s
There is no (140, 178, 5213)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 383413 585709 018632 874026 652117 579591 961697 921440 974592 > 2178 [i]