Best Known (122, 247, s)-Nets in Base 2
(122, 247, 57)-Net over F2 — Constructive and digital
Digital (122, 247, 57)-net over F2, using
- t-expansion [i] based on digital (110, 247, 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
(122, 247, 80)-Net over F2 — Digital
Digital (122, 247, 80)-net over F2, using
- t-expansion [i] based on digital (121, 247, 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
- net from sequence [i] based on digital (121, 79)-sequence over F2, using
(122, 247, 256)-Net over F2 — Upper bound on s (digital)
There is no digital (122, 247, 257)-net over F2, because
- 1 times m-reduction [i] would yield digital (122, 246, 257)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(2246, 257, F2, 124) (dual of [257, 11, 125]-code), but
- residual code [i] would yield linear OA(2122, 132, F2, 62) (dual of [132, 10, 63]-code), but
- residual code [i] would yield linear OA(260, 69, F2, 31) (dual of [69, 9, 32]-code), but
- “BGV†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(260, 69, F2, 31) (dual of [69, 9, 32]-code), but
- residual code [i] would yield linear OA(2122, 132, F2, 62) (dual of [132, 10, 63]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(2246, 257, F2, 124) (dual of [257, 11, 125]-code), but
(122, 247, 260)-Net in Base 2 — Upper bound on s
There is no (122, 247, 261)-net in base 2, because
- 17 times m-reduction [i] would yield (122, 230, 261)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2230, 261, S2, 108), but
- the linear programming bound shows that M ≥ 2423 906907 580468 277479 349413 556067 053430 053216 032374 525434 104378 793213 098031 316992 / 1 326150 802185 > 2230 [i]
- extracting embedded orthogonal array [i] would yield OA(2230, 261, S2, 108), but