MinT - Best Known (228−120, 228, s)-Nets in Base 4

Best Known (228−120, 228, s)-Nets in Base 4

(228−120, 228, 130)-Net over F₄ — Constructive and digital

Digital (108, 228, 130)-net over F₄, using

t-expansion [i] based on digital (105, 228, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(228−120, 228, 144)-Net over F₄ — Digital

Digital (108, 228, 144)-net over F₄, using

t-expansion [i] based on digital (91, 228, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(228−120, 228, 1450)-Net in Base 4 — Upper bound on s

There is no (108, 228, 1451)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 186467 634091 171664 616404 013780 403305 071775 555292 235358 530228 005988 110972 164908 126263 087374 449828 960067 336782 664291 347061 426847 747122 255520 > 4²²⁸ [i]