Best Known (74−53, 74, s)-Nets in Base 4
(74−53, 74, 34)-Net over F4 — Constructive and digital
Digital (21, 74, 34)-net over F4, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- T5 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
(74−53, 74, 44)-Net over F4 — Digital
Digital (21, 74, 44)-net over F4, using
- net from sequence [i] based on digital (21, 43)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 44, using
(74−53, 74, 107)-Net in Base 4 — Upper bound on s
There is no (21, 74, 108)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(474, 108, S4, 53), but
- the linear programming bound shows that M ≥ 3 872107 157622 189057 360618 247446 973402 899851 934866 660124 639981 012835 631104 / 8772 425610 328580 185555 014445 > 474 [i]