MinT - Best Known (102−88, 102, s)-Nets in Base 8

Best Known (102−88, 102, s)-Nets in Base 8

(102−88, 102, 65)-Net over F₈ — Constructive and digital

Digital (14, 102, 65)-net over F₈, using

net from sequence [i] based on digital (14, 64)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ 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]

(102−88, 102, 117)-Net in Base 8 — Upper bound on s

There is no (14, 102, 118)-net in base 8, because

2 times m-reduction [i] would yield (14, 100, 118)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(8¹⁰⁰, 118, S₈, 86), but
  - the linear programming bound shows that MÂ â‰¥ 164566 265892 733580 883230 164819 636579 963677 192824 626175 132024 331250 209356 207369 073818 210714 343572 608863 174656 / 77282 438282 930705 > 8¹⁰⁰ [i]