Best Known (73−30, 73, s)-Nets in Base 16
(73−30, 73, 526)-Net over F16 — Constructive and digital
Digital (43, 73, 526)-net over F16, using
- 1 times m-reduction [i] based on digital (43, 74, 526)-net over F16, using
- trace code for nets [i] based on digital (6, 37, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
- trace code for nets [i] based on digital (6, 37, 263)-net over F256, using
(73−30, 73, 851)-Net over F16 — Digital
Digital (43, 73, 851)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1673, 851, F16, 30) (dual of [851, 778, 31]-code), using
- 200 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 7 times 0, 1, 17 times 0, 1, 37 times 0, 1, 58 times 0, 1, 72 times 0) [i] based on linear OA(1664, 642, F16, 30) (dual of [642, 578, 31]-code), using
- trace code [i] based on linear OA(25632, 321, F256, 30) (dual of [321, 289, 31]-code), using
- extended algebraic-geometric code AGe(F,290P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25632, 321, F256, 30) (dual of [321, 289, 31]-code), using
- 200 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 7 times 0, 1, 17 times 0, 1, 37 times 0, 1, 58 times 0, 1, 72 times 0) [i] based on linear OA(1664, 642, F16, 30) (dual of [642, 578, 31]-code), using
(73−30, 73, 310252)-Net in Base 16 — Upper bound on s
There is no (43, 73, 310253)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 7957 508157 741221 883281 519134 569932 142807 791940 676349 303853 184927 135371 325441 473025 286176 > 1673 [i]