Best Known (44, 44+31, s)-Nets in Base 16
(44, 44+31, 526)-Net over F16 — Constructive and digital
Digital (44, 75, 526)-net over F16, using
- 1 times m-reduction [i] based on digital (44, 76, 526)-net over F16, using
- trace code for nets [i] based on digital (6, 38, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
- trace code for nets [i] based on digital (6, 38, 263)-net over F256, using
(44, 44+31, 838)-Net over F16 — Digital
Digital (44, 75, 838)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1675, 838, F16, 31) (dual of [838, 763, 32]-code), using
- 187 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 6 times 0, 1, 16 times 0, 1, 34 times 0, 1, 54 times 0, 1, 69 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
- 187 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 6 times 0, 1, 16 times 0, 1, 34 times 0, 1, 54 times 0, 1, 69 times 0) [i] based on linear OA(1666, 642, F16, 31) (dual of [642, 576, 32]-code), using
(44, 44+31, 373242)-Net in Base 16 — Upper bound on s
There is no (44, 75, 373243)-net in base 16, because
- 1 times m-reduction [i] would yield (44, 74, 373243)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 127316 289503 285804 059669 444749 432886 370823 868501 614031 997085 354443 119085 994251 445839 060176 > 1674 [i]