MinT - Best Known (88, 88+156, s)-Nets in Base 4

Best Known (88, 88+156, s)-Nets in Base 4

(88, 88+156, 104)-Net over F₄ — Constructive and digital

Digital (88, 244, 104)-net over F₄, using

t-expansion [i] based on digital (73, 244, 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]

(88, 88+156, 129)-Net over F₄ — Digital

Digital (88, 244, 129)-net over F₄, using

t-expansion [i] based on digital (81, 244, 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]

(88, 88+156, 698)-Net in Base 4 — Upper bound on s

There is no (88, 244, 699)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 854 859123 759562 327334 603794 816097 933728 888992 091784 914040 704330 637693 024089 620415 564226 208724 972575 180864 875271 739838 077129 575464 425466 924463 029080 > 4²⁴⁴ [i]