Best Known (105, 105+97, s)-Nets in Base 2
(105, 105+97, 56)-Net over F2 — Constructive and digital
Digital (105, 202, 56)-net over F2, using
- net from sequence [i] based on digital (105, 55)-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 7 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]
(105, 105+97, 65)-Net over F2 — Digital
Digital (105, 202, 65)-net over F2, using
- t-expansion [i] based on digital (95, 202, 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
(105, 105+97, 241)-Net over F2 — Upper bound on s (digital)
There is no digital (105, 202, 242)-net over F2, because
- 1 times m-reduction [i] would yield digital (105, 201, 242)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(2201, 242, F2, 96) (dual of [242, 41, 97]-code), but
- residual code [i] would yield OA(2105, 145, S2, 48), but
- the linear programming bound shows that M ≥ 727 070369 678229 731686 401086 929362 121333 407744 / 17 521374 765895 > 2105 [i]
- residual code [i] would yield OA(2105, 145, S2, 48), but
- extracting embedded orthogonal array [i] would yield linear OA(2201, 242, F2, 96) (dual of [242, 41, 97]-code), but
(105, 105+97, 276)-Net in Base 2 — Upper bound on s
There is no (105, 202, 277)-net in base 2, because
- 1 times m-reduction [i] would yield (105, 201, 277)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 3 643257 707504 809835 518472 024880 822541 482281 600586 542368 050600 > 2201 [i]