Best Known (38, 38+28, s)-Nets in Base 16
(38, 38+28, 524)-Net over F16 — Constructive and digital
Digital (38, 66, 524)-net over F16, using
- trace code for nets [i] based on digital (5, 33, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
(38, 38+28, 687)-Net over F16 — Digital
Digital (38, 66, 687)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1666, 687, F16, 28) (dual of [687, 621, 29]-code), using
- 39 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 0, 1, 9 times 0, 1, 23 times 0) [i] based on linear OA(1660, 642, F16, 28) (dual of [642, 582, 29]-code), using
- trace code [i] based on linear OA(25630, 321, F256, 28) (dual of [321, 291, 29]-code), using
- extended algebraic-geometric code AGe(F,292P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25630, 321, F256, 28) (dual of [321, 291, 29]-code), using
- 39 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 0, 1, 9 times 0, 1, 23 times 0) [i] based on linear OA(1660, 642, F16, 28) (dual of [642, 582, 29]-code), using
(38, 38+28, 191388)-Net in Base 16 — Upper bound on s
There is no (38, 66, 191389)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 29 644425 523800 801728 753812 874440 171614 184731 329555 584691 559710 238489 233249 557816 > 1666 [i]