MinT - Best Known (88, 88+140, s)-Nets in Base 4

Best Known (88, 88+140, s)-Nets in Base 4

(88, 88+140, 104)-Net over F₄ — Constructive and digital

Digital (88, 228, 104)-net over F₄, using

t-expansion [i] based on digital (73, 228, 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+140, 129)-Net over F₄ — Digital

Digital (88, 228, 129)-net over F₄, using

t-expansion [i] based on digital (81, 228, 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+140, 763)-Net in Base 4 — Upper bound on s

There is no (88, 228, 764)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 199240 742168 728674 301518 913377 451828 630404 522890 898291 791925 161319 257337 788326 173789 450283 040258 448704 581845 062156 396711 486513 111601 222586 > 4²²⁸ [i]