Best Known (102−42, 102, s)-Nets in Base 16
(102−42, 102, 532)-Net over F16 — Constructive and digital
Digital (60, 102, 532)-net over F16, using
- trace code for nets [i] based on digital (9, 51, 266)-net over F256, using
- net from sequence [i] based on digital (9, 265)-sequence over F256, using
(102−42, 102, 1088)-Net over F16 — Digital
Digital (60, 102, 1088)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16102, 1088, F16, 42) (dual of [1088, 986, 43]-code), using
- 60 step Varšamov–Edel lengthening with (ri) = (1, 10 times 0, 1, 48 times 0) [i] based on linear OA(16100, 1026, F16, 42) (dual of [1026, 926, 43]-code), using
- trace code [i] based on linear OA(25650, 513, F256, 42) (dual of [513, 463, 43]-code), using
- extended algebraic-geometric code AGe(F,470P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- extended algebraic-geometric code AGe(F,470P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- trace code [i] based on linear OA(25650, 513, F256, 42) (dual of [513, 463, 43]-code), using
- 60 step Varšamov–Edel lengthening with (ri) = (1, 10 times 0, 1, 48 times 0) [i] based on linear OA(16100, 1026, F16, 42) (dual of [1026, 926, 43]-code), using
(102−42, 102, 408293)-Net in Base 16 — Upper bound on s
There is no (60, 102, 408294)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 661 089293 860843 411352 384951 246963 591614 861914 164752 711831 226107 614007 119131 121188 523665 597813 294485 801235 807746 525102 249486 > 16102 [i]