Best Known (42, 73, s)-Nets in Base 16
(42, 73, 524)-Net over F16 — Constructive and digital
Digital (42, 73, 524)-net over F16, using
- 1 times m-reduction [i] based on digital (42, 74, 524)-net over F16, using
- trace code for nets [i] based on digital (5, 37, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
- trace code for nets [i] based on digital (5, 37, 262)-net over F256, using
(42, 73, 711)-Net over F16 — Digital
Digital (42, 73, 711)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1673, 711, F16, 31) (dual of [711, 638, 32]-code), using
- 62 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 6 times 0, 1, 16 times 0, 1, 34 times 0) [i] based on linear OA(1666, 642, F16, 31) (dual of [642, 576, 32]-code), using
- trace code [i] based on linear OA(25633, 321, F256, 31) (dual of [321, 288, 32]-code), using
- extended algebraic-geometric code AGe(F,289P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25633, 321, F256, 31) (dual of [321, 288, 32]-code), using
- 62 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 6 times 0, 1, 16 times 0, 1, 34 times 0) [i] based on linear OA(1666, 642, F16, 31) (dual of [642, 576, 32]-code), using
(42, 73, 257891)-Net in Base 16 — Upper bound on s
There is no (42, 73, 257892)-net in base 16, because
- 1 times m-reduction [i] would yield (42, 72, 257892)-net in base 16, but
- 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]