Best Known (126, 126+124, s)-Nets in Base 2
(126, 126+124, 57)-Net over F2 — Constructive and digital
Digital (126, 250, 57)-net over F2, using
- t-expansion [i] based on digital (110, 250, 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
(126, 126+124, 81)-Net over F2 — Digital
Digital (126, 250, 81)-net over F2, using
- net from sequence [i] based on digital (126, 80)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 126 and N(F) ≥ 81, using
(126, 126+124, 266)-Net over F2 — Upper bound on s (digital)
There is no digital (126, 250, 267)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(2250, 267, F2, 124) (dual of [267, 17, 125]-code), but
- residual code [i] would yield OA(2126, 142, S2, 62), but
- the linear programming bound shows that M ≥ 944964 132939 446113 037791 284838 020323 213312 / 10545 > 2126 [i]
- residual code [i] would yield OA(2126, 142, S2, 62), but
(126, 126+124, 274)-Net in Base 2 — Upper bound on s
There is no (126, 250, 275)-net in base 2, because
- 16 times m-reduction [i] would yield (126, 234, 275)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2234, 275, S2, 108), but
- the linear programming bound shows that M ≥ 275 709011 416343 386283 194427 515396 341112 620119 523157 025502 536288 617777 395593 653660 942336 / 9364 570416 997125 > 2234 [i]
- extracting embedded orthogonal array [i] would yield OA(2234, 275, S2, 108), but