Best Known (97−43, 97, s)-Nets in Base 16
(97−43, 97, 524)-Net over F16 — Constructive and digital
Digital (54, 97, 524)-net over F16, using
- 1 times m-reduction [i] based on digital (54, 98, 524)-net over F16, using
- trace code for nets [i] based on digital (5, 49, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
- trace code for nets [i] based on digital (5, 49, 262)-net over F256, using
(97−43, 97, 690)-Net over F16 — Digital
Digital (54, 97, 690)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1697, 690, F16, 43) (dual of [690, 593, 44]-code), using
- discarding factors / shortening the dual code based on linear OA(1697, 695, F16, 43) (dual of [695, 598, 44]-code), using
- 46 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 24 times 0) [i] based on linear OA(1690, 642, F16, 43) (dual of [642, 552, 44]-code), using
- trace code [i] based on linear OA(25645, 321, F256, 43) (dual of [321, 276, 44]-code), using
- extended algebraic-geometric code AGe(F,277P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25645, 321, F256, 43) (dual of [321, 276, 44]-code), using
- 46 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 24 times 0) [i] based on linear OA(1690, 642, F16, 43) (dual of [642, 552, 44]-code), using
- discarding factors / shortening the dual code based on linear OA(1697, 695, F16, 43) (dual of [695, 598, 44]-code), using
(97−43, 97, 184894)-Net in Base 16 — Upper bound on s
There is no (54, 97, 184895)-net in base 16, because
- 1 times m-reduction [i] would yield (54, 96, 184895)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 39 406088 491650 272236 002645 333285 649227 282788 473643 295246 388754 932330 806036 200986 953781 121113 530605 209461 739464 176926 > 1696 [i]