Best Known (103, 103+98, s)-Nets in Base 2
(103, 103+98, 55)-Net over F2 — Constructive and digital
Digital (103, 201, 55)-net over F2, using
- t-expansion [i] based on digital (100, 201, 55)-net over F2, using
- net from sequence [i] based on digital (100, 54)-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 6 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 (100, 54)-sequence over F2, using
(103, 103+98, 65)-Net over F2 — Digital
Digital (103, 201, 65)-net over F2, using
- t-expansion [i] based on digital (95, 201, 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
(103, 103+98, 228)-Net over F2 — Upper bound on s (digital)
There is no digital (103, 201, 229)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(2201, 229, F2, 98) (dual of [229, 28, 99]-code), but
- residual code [i] would yield OA(2103, 130, S2, 49), but
- 1 times truncation [i] would yield OA(2102, 129, S2, 48), but
- the linear programming bound shows that M ≥ 4505 293676 588367 515344 369298 908326 658048 / 781 535645 > 2102 [i]
- 1 times truncation [i] would yield OA(2102, 129, S2, 48), but
- residual code [i] would yield OA(2103, 130, S2, 49), but
(103, 103+98, 261)-Net in Base 2 — Upper bound on s
There is no (103, 201, 262)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 3 295286 453629 242357 756343 045559 228046 328668 373199 526249 194864 > 2201 [i]