Best Known (31, 53, s)-Nets in Base 16
(31, 53, 522)-Net over F16 — Constructive and digital
Digital (31, 53, 522)-net over F16, using
- 1 times m-reduction [i] based on digital (31, 54, 522)-net over F16, using
- trace code for nets [i] based on digital (4, 27, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- trace code for nets [i] based on digital (4, 27, 261)-net over F256, using
(31, 53, 690)-Net over F16 — Digital
Digital (31, 53, 690)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1653, 690, F16, 22) (dual of [690, 637, 23]-code), using
- 43 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 11 times 0, 1, 27 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
- 43 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 11 times 0, 1, 27 times 0) [i] based on linear OA(1648, 642, F16, 22) (dual of [642, 594, 23]-code), using
(31, 53, 207290)-Net in Base 16 — Upper bound on s
There is no (31, 53, 207291)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 6582 110554 536487 246190 956088 250621 467538 538688 577627 922385 346016 > 1653 [i]