Best Known (65−16, 65, s)-Nets in Base 7
(65−16, 65, 1050)-Net over F7 — Constructive and digital
Digital (49, 65, 1050)-net over F7, using
- net defined by OOA [i] based on linear OOA(765, 1050, F7, 16, 16) (dual of [(1050, 16), 16735, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(765, 8400, F7, 16) (dual of [8400, 8335, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(765, 8403, F7, 16) (dual of [8403, 8338, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(765, 8400, F7, 16) (dual of [8400, 8335, 17]-code), using
(65−16, 65, 7347)-Net over F7 — Digital
Digital (49, 65, 7347)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(765, 7347, F7, 16) (dual of [7347, 7282, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(765, 8403, F7, 16) (dual of [8403, 8338, 17]-code), using
(65−16, 65, 4612750)-Net in Base 7 — Upper bound on s
There is no (49, 65, 4612751)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 8 538335 457563 632308 382226 127437 257511 657175 202626 709201 > 765 [i]