Best Known (132−66, 132, s)-Nets in Base 2
(132−66, 132, 43)-Net over F2 — Constructive and digital
Digital (66, 132, 43)-net over F2, using
- t-expansion [i] based on digital (59, 132, 43)-net over F2, using
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
(132−66, 132, 48)-Net over F2 — Digital
Digital (66, 132, 48)-net over F2, using
- t-expansion [i] based on digital (65, 132, 48)-net over F2, using
- net from sequence [i] based on digital (65, 47)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 65 and N(F) ≥ 48, using
- net from sequence [i] based on digital (65, 47)-sequence over F2, using
(132−66, 132, 143)-Net in Base 2 — Upper bound on s
There is no (66, 132, 144)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2132, 144, S2, 66), but
- the linear programming bound shows that M ≥ 4 616951 154383 293072 271066 673634 231093 035008 / 697 > 2132 [i]