Best Known (12, 12+55, s)-Nets in Base 128
(12, 12+55, 288)-Net over F128 — Constructive and digital
Digital (12, 67, 288)-net over F128, using
- t-expansion [i] based on digital (9, 67, 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+55, 321)-Net over F128 — Digital
Digital (12, 67, 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+55, 12164)-Net in Base 128 — Upper bound on s
There is no (12, 67, 12165)-net in base 128, because
- 1 times m-reduction [i] would yield (12, 66, 12165)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 11 925344 774975 479061 274418 275589 755704 848077 734021 242999 040799 686492 744195 469318 595946 495947 979316 441972 117402 466271 420931 187098 669730 141760 > 12866 [i]