MinT - Best Known (181−96, 181, s)-Nets in Base 4

Best Known (181−96, 181, s)-Nets in Base 4

(181−96, 181, 104)-Net over F₄ — Constructive and digital

Digital (85, 181, 104)-net over F₄, using

t-expansion [i] based on 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]

(181−96, 181, 129)-Net over F₄ — Digital

Digital (85, 181, 129)-net over F₄, using

t-expansion [i] based on digital (81, 181, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(181−96, 181, 1124)-Net in Base 4 — Upper bound on s

There is no (85, 181, 1125)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 409861 331393 651113 057535 291224 236366 616624 202804 046848 519223 514221 417790 034552 435870 311587 612479 779355 041036 > 4¹⁸¹ [i]