Best Known (84−36, 84, s)-Nets in Base 2
(84−36, 84, 35)-Net over F2 — Constructive and digital
Digital (48, 84, 35)-net over F2, using
- net from sequence [i] based on digital (48, 34)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 2 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(84−36, 84, 40)-Net over F2 — Digital
Digital (48, 84, 40)-net over F2, using
- trace code for nets [i] based on digital (6, 42, 20)-net over F4, using
- net from sequence [i] based on digital (6, 19)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 6 and N(F) ≥ 20, using
- net from sequence [i] based on digital (6, 19)-sequence over F4, using
(84−36, 84, 166)-Net in Base 2 — Upper bound on s
There is no (48, 84, 167)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 19 551713 328456 335347 497970 > 284 [i]