Best Known (119, 119+25, s)-Nets in Base 3
(119, 119+25, 820)-Net over F3 — Constructive and digital
Digital (119, 144, 820)-net over F3, using
- net defined by OOA [i] based on linear OOA(3144, 820, F3, 25, 25) (dual of [(820, 25), 20356, 26]-NRT-code), using
(119, 119+25, 4920)-Net over F3 — Digital
Digital (119, 144, 4920)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3144, 4920, F3, 2, 25) (dual of [(4920, 2), 9696, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3144, 9840, F3, 25) (dual of [9840, 9696, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3144, 9841, F3, 25) (dual of [9841, 9697, 26]-code), using
- OOA 2-folding [i] based on linear OA(3144, 9840, F3, 25) (dual of [9840, 9696, 26]-code), using
(119, 119+25, 1282396)-Net in Base 3 — Upper bound on s
There is no (119, 144, 1282397)-net in base 3, because
- 1 times m-reduction [i] would yield (119, 143, 1282397)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 169 176345 345720 570416 323268 464496 333492 729072 351597 877710 896165 913841 > 3143 [i]