Best Known (82−21, 82, s)-Nets in Base 2
(82−21, 82, 84)-Net over F2 — Constructive and digital
Digital (61, 82, 84)-net over F2, using
- 2 times m-reduction [i] based on digital (61, 84, 84)-net over F2, using
- trace code for nets [i] based on digital (5, 28, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- trace code for nets [i] based on digital (5, 28, 28)-net over F8, using
(82−21, 82, 137)-Net over F2 — Digital
Digital (61, 82, 137)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(282, 137, F2, 2, 21) (dual of [(137, 2), 192, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(282, 274, F2, 21) (dual of [274, 192, 22]-code), using
(82−21, 82, 1228)-Net in Base 2 — Upper bound on s
There is no (61, 82, 1229)-net in base 2, because
- 1 times m-reduction [i] would yield (61, 81, 1229)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 2 434625 062755 308347 912974 > 281 [i]