Best Known (121, 121+120, s)-Nets in Base 2
(121, 121+120, 57)-Net over F2 — Constructive and digital
Digital (121, 241, 57)-net over F2, using
- t-expansion [i] based on digital (110, 241, 57)-net over F2, using
- net from sequence [i] based on digital (110, 56)-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 8 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 (110, 56)-sequence over F2, using
(121, 121+120, 80)-Net over F2 — Digital
Digital (121, 241, 80)-net over F2, using
- net from sequence [i] based on digital (121, 79)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 121 and N(F) ≥ 80, using
(121, 121+120, 256)-Net over F2 — Upper bound on s (digital)
There is no digital (121, 241, 257)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(2241, 257, F2, 120) (dual of [257, 16, 121]-code), but
- residual code [i] would yield OA(2121, 136, S2, 60), but
- the linear programming bound shows that M ≥ 579798 617937 414024 433657 409237 804061 294592 / 216783 > 2121 [i]
- residual code [i] would yield OA(2121, 136, S2, 60), but
(121, 121+120, 258)-Net in Base 2 — Upper bound on s
There is no (121, 241, 259)-net in base 2, because
- 12 times m-reduction [i] would yield (121, 229, 259)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2229, 259, S2, 108), but
- the linear programming bound shows that M ≥ 17498 495097 789040 453213 386774 622994 352540 479460 641070 835741 390745 701581 780259 176448 / 19 797109 545047 > 2229 [i]
- extracting embedded orthogonal array [i] would yield OA(2229, 259, S2, 108), but