Best Known (46, 75, s)-Nets in Base 7
(46, 75, 116)-Net over F7 — Constructive and digital
Digital (46, 75, 116)-net over F7, using
- 1 times m-reduction [i] based on digital (46, 76, 116)-net over F7, using
- trace code for nets [i] based on digital (8, 38, 58)-net over F49, using
- net from sequence [i] based on digital (8, 57)-sequence over F49, using
- trace code for nets [i] based on digital (8, 38, 58)-net over F49, using
(46, 75, 362)-Net over F7 — Digital
Digital (46, 75, 362)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(775, 362, F7, 29) (dual of [362, 287, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(775, 363, F7, 29) (dual of [363, 288, 30]-code), using
- 17 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 0, 1, 12 times 0) [i] based on linear OA(773, 344, F7, 29) (dual of [344, 271, 30]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 344 | 76−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- 17 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 0, 1, 12 times 0) [i] based on linear OA(773, 344, F7, 29) (dual of [344, 271, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(775, 363, F7, 29) (dual of [363, 288, 30]-code), using
(46, 75, 29520)-Net in Base 7 — Upper bound on s
There is no (46, 75, 29521)-net in base 7, because
- 1 times m-reduction [i] would yield (46, 74, 29521)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 344 637804 231735 511853 534288 509852 466157 036135 807670 614602 734321 > 774 [i]