Best Known (243−144, 243, s)-Nets in Base 2
(243−144, 243, 54)-Net over F2 — Constructive and digital
Digital (99, 243, 54)-net over F2, using
- t-expansion [i] based on digital (95, 243, 54)-net over F2, using
- net from sequence [i] based on digital (95, 53)-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 5 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]
- net from sequence [i] based on digital (95, 53)-sequence over F2, using
(243−144, 243, 65)-Net over F2 — Digital
Digital (99, 243, 65)-net over F2, using
- t-expansion [i] based on digital (95, 243, 65)-net over F2, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 95 and N(F) ≥ 65, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
(243−144, 243, 194)-Net in Base 2 — Upper bound on s
There is no (99, 243, 195)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 15 614406 793271 553463 579779 250287 203843 979811 053026 871572 976336 719054 820176 > 2243 [i]