Best Known (111−100, 111, s)-Nets in Base 5
(111−100, 111, 32)-Net over F5 — Constructive and digital
Digital (11, 111, 32)-net over F5, using
- net from sequence [i] based on digital (11, 31)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 11 and N(F) ≥ 32, using
(111−100, 111, 63)-Net over F5 — Upper bound on s (digital)
There is no digital (11, 111, 64)-net over F5, because
- 50 times m-reduction [i] would yield digital (11, 61, 64)-net over F5, but
- extracting embedded orthogonal array [i] would yield linear OA(561, 64, F5, 50) (dual of [64, 3, 51]-code), but
(111−100, 111, 64)-Net in Base 5 — Upper bound on s
There is no (11, 111, 65)-net in base 5, because
- 52 times m-reduction [i] would yield (11, 59, 65)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(559, 65, S5, 48), but
- the linear programming bound shows that M ≥ 802 309607 639273 281165 515072 643756 866455 078125 / 3773 > 559 [i]
- extracting embedded orthogonal array [i] would yield OA(559, 65, S5, 48), but