Best Known (5, 5+80, s)-Nets in Base 16
(5, 5+80, 49)-Net over F16 — Constructive and digital
Digital (5, 85, 49)-net over F16, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 5 and N(F) ≥ 49, using
(5, 5+80, 91)-Net over F16 — Upper bound on s (digital)
There is no digital (5, 85, 92)-net over F16, because
- extracting embedded orthogonal array [i] would yield linear OA(1685, 92, F16, 80) (dual of [92, 7, 81]-code), but
- construction Y1 [i] would yield
- OA(1684, 86, S16, 80), but
- the (dual) Plotkin bound shows that M ≥ 4 479489 484355 608421 114884 561136 888556 243290 994469 299069 799978 201927 583742 360321 890761 754986 543214 231552 / 27 > 1684 [i]
- OA(167, 92, S16, 6), but
- discarding factors would yield OA(167, 80, S16, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 278 002201 > 167 [i]
- discarding factors would yield OA(167, 80, S16, 6), but
- OA(1684, 86, S16, 80), but
- construction Y1 [i] would yield
(5, 5+80, 95)-Net in Base 16 — Upper bound on s
There is no (5, 85, 96)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1685, 96, S16, 80), but
- the linear programming bound shows that M ≥ 49408 180156 672705 434036 570631 075011 964541 450150 935399 783715 239941 326736 085785 914736 627685 524308 141949 248537 100288 / 17371 208413 > 1685 [i]