Best Known (28, 28+126, s)-Nets in Base 8
(28, 28+126, 65)-Net over F8 — Constructive and digital
Digital (28, 154, 65)-net over F8, using
- t-expansion [i] based on digital (14, 154, 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
(28, 28+126, 97)-Net over F8 — Digital
Digital (28, 154, 97)-net over F8, using
- net from sequence [i] based on digital (28, 96)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 28 and N(F) ≥ 97, using
(28, 28+126, 520)-Net in Base 8 — Upper bound on s
There is no (28, 154, 521)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 12 235740 000328 111831 332990 172695 232660 594524 400173 857673 593744 125534 511450 568169 978860 934849 138508 025270 888035 956979 142597 718257 264496 880128 > 8154 [i]