Best Known (72−30, 72, s)-Nets in Base 16
(72−30, 72, 526)-Net over F16 — Constructive and digital
Digital (42, 72, 526)-net over F16, using
- trace code for nets [i] based on digital (6, 36, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
(72−30, 72, 777)-Net over F16 — Digital
Digital (42, 72, 777)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1672, 777, F16, 30) (dual of [777, 705, 31]-code), using
- 127 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) [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
- 127 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) [i] based on linear OA(1664, 642, F16, 30) (dual of [642, 578, 31]-code), using
(72−30, 72, 257891)-Net in Base 16 — Upper bound on s
There is no (42, 72, 257892)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 497 323985 220407 746776 306579 437699 047213 310040 758493 012783 711507 601418 092726 809673 351576 > 1672 [i]