Best Known (98−79, 98, s)-Nets in Base 8
(98−79, 98, 65)-Net over F8 — Constructive and digital
Digital (19, 98, 65)-net over F8, using
- t-expansion [i] based on digital (14, 98, 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
(98−79, 98, 363)-Net in Base 8 — Upper bound on s
There is no (19, 98, 364)-net in base 8, because
- 1 times m-reduction [i] would yield (19, 97, 364)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 4153 510629 287629 486521 079954 399335 791240 439084 140394 527228 924749 818862 406418 750013 265106 > 897 [i]