Best Known (44, 44+32, s)-Nets in Base 16
(44, 44+32, 526)-Net over F16 — Constructive and digital
Digital (44, 76, 526)-net over F16, using
- trace code for nets [i] based on digital (6, 38, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
(44, 44+32, 760)-Net over F16 — Digital
Digital (44, 76, 760)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1676, 760, F16, 32) (dual of [760, 684, 33]-code), using
- 110 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 5 times 0, 1, 15 times 0, 1, 32 times 0, 1, 51 times 0) [i] based on linear OA(1668, 642, F16, 32) (dual of [642, 574, 33]-code), using
- trace code [i] based on linear OA(25634, 321, F256, 32) (dual of [321, 287, 33]-code), using
- extended algebraic-geometric code AGe(F,288P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25634, 321, F256, 32) (dual of [321, 287, 33]-code), using
- 110 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 5 times 0, 1, 15 times 0, 1, 32 times 0, 1, 51 times 0) [i] based on linear OA(1668, 642, F16, 32) (dual of [642, 574, 33]-code), using
(44, 44+32, 237684)-Net in Base 16 — Upper bound on s
There is no (44, 76, 237685)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 32 592628 576955 264055 887863 342556 118401 305345 095188 374070 242531 709791 211742 110380 764528 873151 > 1676 [i]