Best Known (70−30, 70, s)-Nets in Base 16
(70−30, 70, 524)-Net over F16 — Constructive and digital
Digital (40, 70, 524)-net over F16, using
- trace code for nets [i] based on digital (5, 35, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
(70−30, 70, 678)-Net over F16 — Digital
Digital (40, 70, 678)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1670, 678, F16, 30) (dual of [678, 608, 31]-code), using
- 30 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 7 times 0, 1, 17 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
- 30 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 7 times 0, 1, 17 times 0) [i] based on linear OA(1664, 642, F16, 30) (dual of [642, 578, 31]-code), using
(70−30, 70, 178189)-Net in Base 16 — Upper bound on s
There is no (40, 70, 178190)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 1 942726 448804 307192 670055 898406 753929 253218 066157 914191 458083 699330 476297 800977 093376 > 1670 [i]