Best Known (18, 18+77, s)-Nets in Base 16
(18, 18+77, 65)-Net over F16 — Constructive and digital
Digital (18, 95, 65)-net over F16, using
- t-expansion [i] based on digital (6, 95, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(18, 18+77, 113)-Net over F16 — Digital
Digital (18, 95, 113)-net over F16, using
- net from sequence [i] based on digital (18, 112)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 18 and N(F) ≥ 113, using
(18, 18+77, 932)-Net in Base 16 — Upper bound on s
There is no (18, 95, 933)-net in base 16, because
- 1 times m-reduction [i] would yield (18, 94, 933)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 156450 858318 091701 828434 758683 988029 661219 587759 481125 991719 034351 040101 463734 555224 966534 439980 952220 260722 636736 > 1694 [i]