Best Known (29, 29+11, s)-Nets in Base 5
(29, 29+11, 312)-Net over F5 — Constructive and digital
Digital (29, 40, 312)-net over F5, using
- net defined by OOA [i] based on linear OOA(540, 312, F5, 11, 11) (dual of [(312, 11), 3392, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(540, 1561, F5, 11) (dual of [1561, 1521, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(540, 1562, F5, 11) (dual of [1562, 1522, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(540, 1561, F5, 11) (dual of [1561, 1521, 12]-code), using
(29, 29+11, 1102)-Net over F5 — Digital
Digital (29, 40, 1102)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(540, 1102, F5, 11) (dual of [1102, 1062, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(540, 1562, F5, 11) (dual of [1562, 1522, 12]-code), using
(29, 29+11, 184388)-Net in Base 5 — Upper bound on s
There is no (29, 40, 184389)-net in base 5, because
- 1 times m-reduction [i] would yield (29, 39, 184389)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 1818 997193 184861 453663 443013 > 539 [i]