Best Known (102−45, 102, s)-Nets in Base 16
(102−45, 102, 526)-Net over F16 — Constructive and digital
Digital (57, 102, 526)-net over F16, using
- trace code for nets [i] based on digital (6, 51, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
(102−45, 102, 735)-Net over F16 — Digital
Digital (57, 102, 735)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16102, 735, F16, 45) (dual of [735, 633, 46]-code), using
- 85 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 13 times 0, 1, 25 times 0, 1, 36 times 0) [i] based on linear OA(1694, 642, F16, 45) (dual of [642, 548, 46]-code), using
- trace code [i] based on linear OA(25647, 321, F256, 45) (dual of [321, 274, 46]-code), using
- extended algebraic-geometric code AGe(F,275P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25647, 321, F256, 45) (dual of [321, 274, 46]-code), using
- 85 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 13 times 0, 1, 25 times 0, 1, 36 times 0) [i] based on linear OA(1694, 642, F16, 45) (dual of [642, 548, 46]-code), using
(102−45, 102, 203583)-Net in Base 16 — Upper bound on s
There is no (57, 102, 203584)-net in base 16, because
- 1 times m-reduction [i] would yield (57, 101, 203584)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 41 320240 639063 729881 885944 258546 137284 436683 697304 934110 152309 623373 155633 144440 950760 140225 310430 675631 628054 420395 127221 > 16101 [i]