Best Known (65, 112, s)-Nets in Base 16
(65, 112, 532)-Net over F16 — Constructive and digital
Digital (65, 112, 532)-net over F16, using
- trace code for nets [i] based on digital (9, 56, 266)-net over F256, using
- net from sequence [i] based on digital (9, 265)-sequence over F256, using
(65, 112, 1056)-Net over F16 — Digital
Digital (65, 112, 1056)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16112, 1056, F16, 47) (dual of [1056, 944, 48]-code), using
- 28 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 1, 24 times 0) [i] based on linear OA(16110, 1026, F16, 47) (dual of [1026, 916, 48]-code), using
- trace code [i] based on linear OA(25655, 513, F256, 47) (dual of [513, 458, 48]-code), using
- extended algebraic-geometric code AGe(F,465P) [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,465P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- trace code [i] based on linear OA(25655, 513, F256, 47) (dual of [513, 458, 48]-code), using
- 28 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 1, 24 times 0) [i] based on linear OA(16110, 1026, F16, 47) (dual of [1026, 916, 48]-code), using
(65, 112, 406948)-Net in Base 16 — Upper bound on s
There is no (65, 112, 406949)-net in base 16, because
- 1 times m-reduction [i] would yield (65, 111, 406949)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 45 428858 999470 524892 026424 873802 790842 827106 634565 114504 178725 122103 961788 980124 210774 255517 697910 920642 470788 693796 336336 901988 298656 > 16111 [i]