Best Known (15, 15+46, s)-Nets in Base 4
(15, 15+46, 33)-Net over F4 — Constructive and digital
Digital (15, 61, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
(15, 15+46, 35)-Net over F4 — Digital
Digital (15, 61, 35)-net over F4, using
- net from sequence [i] based on digital (15, 34)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 35, using
(15, 15+46, 69)-Net over F4 — Upper bound on s (digital)
There is no digital (15, 61, 70)-net over F4, because
- extracting embedded orthogonal array [i] would yield linear OA(461, 70, F4, 46) (dual of [70, 9, 47]-code), but
- “Gur†bound on codes from Brouwer’s database [i]
(15, 15+46, 70)-Net in Base 4 — Upper bound on s
There is no (15, 61, 71)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(461, 71, S4, 46), but
- the linear programming bound shows that M ≥ 174 709133 954015 909665 219644 446048 162198 585344 / 19 840815 > 461 [i]