Best Known (50−21, 50, s)-Nets in Base 7
(50−21, 50, 108)-Net over F7 — Constructive and digital
Digital (29, 50, 108)-net over F7, using
- trace code for nets [i] based on digital (4, 25, 54)-net over F49, using
- net from sequence [i] based on digital (4, 53)-sequence over F49, using
(50−21, 50, 190)-Net over F7 — Digital
Digital (29, 50, 190)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(750, 190, F7, 21) (dual of [190, 140, 22]-code), using
- 30 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 10 times 0, 1, 14 times 0) [i] based on linear OA(746, 156, F7, 21) (dual of [156, 110, 22]-code), using
- trace code [i] based on linear OA(4923, 78, F49, 21) (dual of [78, 55, 22]-code), using
- extended algebraic-geometric code AGe(F,56P) [i] based on function field F/F49 with g(F) = 2 and N(F) ≥ 78, using
- trace code [i] based on linear OA(4923, 78, F49, 21) (dual of [78, 55, 22]-code), using
- 30 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 10 times 0, 1, 14 times 0) [i] based on linear OA(746, 156, F7, 21) (dual of [156, 110, 22]-code), using
(50−21, 50, 10436)-Net in Base 7 — Upper bound on s
There is no (29, 50, 10437)-net in base 7, because
- 1 times m-reduction [i] would yield (29, 49, 10437)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 257081 632906 171677 430607 016094 057565 768473 > 749 [i]