Best Known (100−44, 100, s)-Nets in Base 16
(100−44, 100, 526)-Net over F16 — Constructive and digital
Digital (56, 100, 526)-net over F16, using
- trace code for nets [i] based on digital (6, 50, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
(100−44, 100, 734)-Net over F16 — Digital
Digital (56, 100, 734)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16100, 734, F16, 44) (dual of [734, 634, 45]-code), using
- 84 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 25 times 0, 1, 36 times 0) [i] based on linear OA(1692, 642, F16, 44) (dual of [642, 550, 45]-code), using
- trace code [i] based on linear OA(25646, 321, F256, 44) (dual of [321, 275, 45]-code), using
- extended algebraic-geometric code AGe(F,276P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25646, 321, F256, 44) (dual of [321, 275, 45]-code), using
- 84 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 25 times 0, 1, 36 times 0) [i] based on linear OA(1692, 642, F16, 44) (dual of [642, 550, 45]-code), using
(100−44, 100, 179475)-Net in Base 16 — Upper bound on s
There is no (56, 100, 179476)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 2 582370 339125 410486 825272 197442 022295 468727 497777 287689 449047 987094 161795 283511 928796 763996 270260 157637 926659 946791 429056 > 16100 [i]