MinT - Best Known (105, 105+112, s)-Nets in Base 4

Best Known (105, 105+112, s)-Nets in Base 4

(105, 105+112, 130)-Net over F₄ — Constructive and digital

Digital (105, 217, 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]

(105, 105+112, 144)-Net over F₄ — Digital

Digital (105, 217, 144)-net over F₄, using

t-expansion [i] based on digital (91, 217, 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]

(105, 105+112, 1512)-Net in Base 4 — Upper bound on s

There is no (105, 217, 1513)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 45800 878938 854813 957886 415066 518507 251746 449397 520413 410421 846348 642375 054241 300385 102717 058244 801084 024297 117399 781836 564375 498380 > 4²¹⁷ [i]