Best Known (48−20, 48, s)-Nets in Base 16
(48−20, 48, 522)-Net over F16 — Constructive and digital
Digital (28, 48, 522)-net over F16, using
- trace code for nets [i] based on digital (4, 24, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
(48−20, 48, 665)-Net over F16 — Digital
Digital (28, 48, 665)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1648, 665, F16, 20) (dual of [665, 617, 21]-code), using
- 19 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 0, 1, 14 times 0) [i] based on linear OA(1644, 642, F16, 20) (dual of [642, 598, 21]-code), using
- trace code [i] based on linear OA(25622, 321, F256, 20) (dual of [321, 299, 21]-code), using
- extended algebraic-geometric code AGe(F,300P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25622, 321, F256, 20) (dual of [321, 299, 21]-code), using
- 19 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 0, 1, 14 times 0) [i] based on linear OA(1644, 642, F16, 20) (dual of [642, 598, 21]-code), using
(48−20, 48, 181822)-Net in Base 16 — Upper bound on s
There is no (28, 48, 181823)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 6277 130466 174162 118079 303678 677558 966173 560026 504875 480451 > 1648 [i]