Best Known (207−117, 207, s)-Nets in Base 2
(207−117, 207, 53)-Net over F2 — Constructive and digital
Digital (90, 207, 53)-net over F2, using
- net from sequence [i] based on digital (90, 52)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 4 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
(207−117, 207, 57)-Net over F2 — Digital
Digital (90, 207, 57)-net over F2, using
- t-expansion [i] based on digital (83, 207, 57)-net over F2, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 83 and N(F) ≥ 57, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
(207−117, 207, 187)-Net in Base 2 — Upper bound on s
There is no (90, 207, 188)-net in base 2, because
- 1 times m-reduction [i] would yield (90, 206, 188)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 106 674151 365536 863915 411038 803626 656159 695217 939145 075309 814391 > 2206 [i]