Best Known (59−25, 59, s)-Nets in Base 16
(59−25, 59, 522)-Net over F16 — Constructive and digital
Digital (34, 59, 522)-net over F16, using
- 1 times m-reduction [i] based on digital (34, 60, 522)-net over F16, using
- trace code for nets [i] based on digital (4, 30, 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, 30, 261)-net over F256, using
(59−25, 59, 672)-Net over F16 — Digital
Digital (34, 59, 672)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1659, 672, F16, 25) (dual of [672, 613, 26]-code), using
- 25 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 6 times 0, 1, 15 times 0) [i] based on linear OA(1654, 642, F16, 25) (dual of [642, 588, 26]-code), using
- trace code [i] based on linear OA(25627, 321, F256, 25) (dual of [321, 294, 26]-code), using
- extended algebraic-geometric code AGe(F,295P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25627, 321, F256, 25) (dual of [321, 294, 26]-code), using
- 25 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 6 times 0, 1, 15 times 0) [i] based on linear OA(1654, 642, F16, 25) (dual of [642, 588, 26]-code), using
(59−25, 59, 232901)-Net in Base 16 — Upper bound on s
There is no (34, 59, 232902)-net in base 16, because
- 1 times m-reduction [i] would yield (34, 58, 232902)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 6902 044091 117905 932426 559253 346985 805693 886433 006273 502541 621127 352536 > 1658 [i]