Best Known (4, 4+4, s)-Nets in Base 5
(4, 4+4, 78)-Net over F5 — Constructive and digital
Digital (4, 8, 78)-net over F5, using
(4, 4+4, 98)-Net over F5 — Digital
Digital (4, 8, 98)-net over F5, using
- net defined by OOA [i] based on linear OOA(58, 98, F5, 4, 4) (dual of [(98, 4), 384, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(58, 98, F5, 3, 4) (dual of [(98, 3), 286, 5]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(58, 98, F5, 4) (dual of [98, 90, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(58, 124, F5, 4) (dual of [124, 116, 5]-code), using
- a “DaH†code from Brouwer’s database [i]
- discarding factors / shortening the dual code based on linear OA(58, 124, F5, 4) (dual of [124, 116, 5]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(58, 98, F5, 4) (dual of [98, 90, 5]-code), using
- appending kth column [i] based on linear OOA(58, 98, F5, 3, 4) (dual of [(98, 3), 286, 5]-NRT-code), using
(4, 4+4, 219)-Net in Base 5 — Upper bound on s
There is no (4, 8, 220)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 390721 > 58 [i]