Best Known (12, 12+49, s)-Nets in Base 128
(12, 12+49, 288)-Net over F128 — Constructive and digital
Digital (12, 61, 288)-net over F128, using
- t-expansion [i] based on digital (9, 61, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
(12, 12+49, 321)-Net over F128 — Digital
Digital (12, 61, 321)-net over F128, using
- net from sequence [i] based on digital (12, 320)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 12 and N(F) ≥ 321, using
(12, 12+49, 14296)-Net in Base 128 — Upper bound on s
There is no (12, 61, 14297)-net in base 128, because
- 1 times m-reduction [i] would yield (12, 60, 14297)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 2 710057 773470 227732 318168 804412 014562 704925 463640 439216 304938 586812 555637 072242 329981 740742 536201 143153 581413 232154 400445 194637 > 12860 [i]