Best Known (62, 62+83, s)-Nets in Base 8
(62, 62+83, 99)-Net over F8 — Constructive and digital
Digital (62, 145, 99)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (7, 48, 34)-net over F8, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- digital (14, 97, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- digital (7, 48, 34)-net over F8, using
(62, 62+83, 144)-Net over F8 — Digital
Digital (62, 145, 144)-net over F8, using
- t-expansion [i] based on digital (45, 145, 144)-net over F8, using
- net from sequence [i] based on digital (45, 143)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 45 and N(F) ≥ 144, using
- net from sequence [i] based on digital (45, 143)-sequence over F8, using
(62, 62+83, 3399)-Net in Base 8 — Upper bound on s
There is no (62, 145, 3400)-net in base 8, because
- 1 times m-reduction [i] would yield (62, 144, 3400)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 11215 576194 289904 633629 546467 407992 795184 017952 051266 535185 692202 588465 911222 033131 955939 204460 771581 690298 763434 809897 967879 420888 > 8144 [i]