Best Known (6, 6+4, s)-Nets in Base 5
(6, 6+4, 137)-Net over F5 — Constructive and digital
Digital (6, 10, 137)-net over F5, using
- 51 times duplication [i] based on digital (5, 9, 137)-net over F5, using
(6, 6+4, 150)-Net over F5 — Digital
Digital (6, 10, 150)-net over F5, using
- net defined by OOA [i] based on linear OOA(510, 150, F5, 4, 4) (dual of [(150, 4), 590, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(510, 150, F5, 3, 4) (dual of [(150, 3), 440, 5]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(510, 150, F5, 4) (dual of [150, 140, 5]-code), using
- 12 step Varšamov–Edel lengthening with (ri) = (1, 11 times 0) [i] based on linear OA(59, 137, F5, 4) (dual of [137, 128, 5]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(510, 150, F5, 4) (dual of [150, 140, 5]-code), using
- appending kth column [i] based on linear OOA(510, 150, F5, 3, 4) (dual of [(150, 3), 440, 5]-NRT-code), using
(6, 6+4, 1103)-Net in Base 5 — Upper bound on s
There is no (6, 10, 1104)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 9 768193 > 510 [i]