Best Known (126, 260, s)-Nets in Base 2
(126, 260, 57)-Net over F2 — Constructive and digital
Digital (126, 260, 57)-net over F2, using
- t-expansion [i] based on digital (110, 260, 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, 260, 81)-Net over F2 — Digital
Digital (126, 260, 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, 260, 261)-Net over F2 — Upper bound on s (digital)
There is no digital (126, 260, 262)-net over F2, because
- 6 times m-reduction [i] would yield digital (126, 254, 262)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(2254, 262, F2, 128) (dual of [262, 8, 129]-code), but
(126, 260, 266)-Net in Base 2 — Upper bound on s
There is no (126, 260, 267)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2260, 267, S2, 134), but
- the (dual) Plotkin bound shows that M ≥ 118 571099 379011 784113 736688 648896 417641 748464 297615 937576 404566 024103 044751 294464 / 45 > 2260 [i]