MinT - Best Known (181−108, 181, s)-Nets in Base 4

Best Known (181−108, 181, s)-Nets in Base 4

(181−108, 181, 104)-Net over F₄ — Constructive and digital

Digital (73, 181, 104)-net over F₄, using

net from sequence [i] based on digital (73, 103)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
  - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(181−108, 181, 112)-Net over F₄ — Digital

Digital (73, 181, 112)-net over F₄, using

net from sequence [i] based on digital (73, 111)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
  - Drinfeld modules of rank 1 [i]

(181−108, 181, 685)-Net in Base 4 — Upper bound on s

There is no (73, 181, 686)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 102115 261613 243083 754735 810000 560429 314156 857076 875779 575304 262040 223889 081345 798714 479334 286468 271681 452768 > 4¹⁸¹ [i]