Best Known (32, 54, s)-Nets in Base 16
(32, 54, 524)-Net over F16 — Constructive and digital
Digital (32, 54, 524)-net over F16, using
- trace code for nets [i] based on digital (5, 27, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
(32, 54, 748)-Net over F16 — Digital
Digital (32, 54, 748)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1654, 748, F16, 22) (dual of [748, 694, 23]-code), using
- 100 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 11 times 0, 1, 27 times 0, 1, 56 times 0) [i] based on linear OA(1648, 642, F16, 22) (dual of [642, 594, 23]-code), using
- trace code [i] based on linear OA(25624, 321, F256, 22) (dual of [321, 297, 23]-code), using
- extended algebraic-geometric code AGe(F,298P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25624, 321, F256, 22) (dual of [321, 297, 23]-code), using
- 100 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 11 times 0, 1, 27 times 0, 1, 56 times 0) [i] based on linear OA(1648, 642, F16, 22) (dual of [642, 594, 23]-code), using
(32, 54, 266715)-Net in Base 16 — Upper bound on s
There is no (32, 54, 266716)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 105315 085348 550434 859838 015479 457330 165768 866041 209107 798831 438641 > 1654 [i]