Best Known (105, 105+98, s)-Nets in Base 2
(105, 105+98, 56)-Net over F2 — Constructive and digital
Digital (105, 203, 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+98, 65)-Net over F2 — Digital
Digital (105, 203, 65)-net over F2, using
- t-expansion [i] based on digital (95, 203, 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+98, 239)-Net over F2 — Upper bound on s (digital)
There is no digital (105, 203, 240)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(2203, 240, F2, 98) (dual of [240, 37, 99]-code), but
- residual code [i] would yield OA(2105, 141, S2, 49), but
- 1 times truncation [i] would yield OA(2104, 140, S2, 48), but
- the linear programming bound shows that M ≥ 906615 640616 170781 657520 759485 197602 258944 / 38102 739675 > 2104 [i]
- 1 times truncation [i] would yield OA(2104, 140, S2, 48), but
- residual code [i] would yield OA(2105, 141, S2, 49), but
(105, 105+98, 271)-Net in Base 2 — Upper bound on s
There is no (105, 203, 272)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 14 707080 774480 152183 870353 276014 868914 961063 099431 603560 497776 > 2203 [i]